Sharing power, simulation, and modeling noise
Peter Ralph
27 November 2018 – Advanced Biological Statistics
Baseball
Baseball
We have a dataset of batting averages of baseball players, having
- name
- position
- number of at bats
- number of hits
## Player PriPos Hits AtBats PlayerNumber PriPosNumber
## 1 Fernando Abad Pitcher 1 7 1 1
## 2 Bobby Abreu Left Field 53 219 2 7
## 3 Tony Abreu 2nd Base 18 70 3 4
## 4 Dustin Ackley 2nd Base 137 607 4 4
## 5 Matt Adams 1st Base 21 86 5 3
## 6 Nathan Adcock Pitcher 0 1 6 1The overall batting average of the 948 players is 0.2546597.
Here is the average by position.
batting %>% group_by(PriPos) %>%
summarise(num=n(), BatAvg=sum(Hits)/sum(AtBats)) %>%
select(PriPos, num, BatAvg)## # A tibble: 9 x 3
## PriPos num BatAvg
## <fct> <int> <dbl>
## 1 1st Base 81 0.259
## 2 2nd Base 72 0.256
## 3 3rd Base 75 0.265
## 4 Catcher 103 0.247
## 5 Center Field 67 0.264
## 6 Left Field 103 0.259
## 7 Pitcher 324 0.129
## 8 Right Field 60 0.264
## 9 Shortstop 63 0.255Questions?
What’s the overall batting average?
Do some positions tend to be better batters?
How much variation is there?
Everyone is the same
first_model <- "
data {
int N;
int hits[N];
int at_bats[N];
}
parameters {
real<lower=0, upper=1> theta;
}
model {
hits ~ binomial(at_bats, theta);
theta ~ beta(1, 1);
} "
first_fit <- stan(model_code=first_model, chains=3, iter=1000,
data=list(N=nrow(batting),
hits=batting$Hits,
at_bats=batting$AtBats))
Every pitcher is the same
pos_model <- "
data {
int N;
int hits[N];
int at_bats[N];
int npos; // number of positions
int position[N];
}
parameters {
real<lower=0, upper=1> theta[npos];
}
model {
real theta_vec[N];
for (k in 1:N) {
theta_vec[k] = theta[position[k]];
}
hits ~ binomial(at_bats, theta_vec);
theta ~ beta(1, 1);
} "
pos_fit <- stan(model_code=pos_model, chains=3, iter=1000,
data=list(N=nrow(batting),
hits=batting$Hits,
at_bats=batting$AtBats,
npos=nlevels(batting$PriPos),
position=as.numeric(batting$PriPos)))theta_samples <- extract(pos_fit)$theta
layout(matrix(1:9, nrow=3))
for (k in 1:ncol(theta_samples)) {
hist(theta_samples[,k], main=levels(batting$PriPos)[k], xlim=c(0.1, 0.3),
col=adjustcolor('red',0.6), xlab='batting avg', freq=FALSE)
}
Your turn : Every individual different.
\[\begin{aligned} Z_i &\sim \Binom(N_i, \theta_i) \\ \theta_i &\sim \Beta(\alpha_{p_i}, \beta_{p_i}) \\ \alpha_p &= \mu_p \kappa_p \\ \beta_p &= (1-\mu_p) \kappa_p \\ \mu_p &\sim \Beta(1, 1) \\ \kappa_p &\sim \Gam(0.1, 0.1) . \end{aligned}\]
Variable types in Stan:
int x; // an integer
int y[10]; // ten integers
real z; // a number
real z[2,5]; // a 2x5 array of numbers
vector u[10]; // length 10 vector
matrix v[10,10]; // 10x10 matrix
vector[10] w[10]; // ten length 10 vectors- don’t forget the
; - make sure R types match
- read the error messages
Stochastic minute
Exponential, and Gamma
If \(T \sim \Exp(\text{rate}=\lambda)\), then
\[\begin{aligned} \P\{ T \in dt \} = \lambda e^{-\lambda t} dt . \end{aligned}\]
\(T\) can be any nonnegative real number.
\(T\) is memoryless: \[\begin{aligned} \P\{ T > x + y \given T > x \} = \P\{ T > y \} . \end{aligned}\]
A machine produces \(n\) widgets per second; each widget has probability \(\lambda/n\) of being broken. The time until the first broken widget appears (in seconds) is approximately \(\sim \Exp(\lambda)\).
If \(S \sim \Gam(\text{shape}=\alpha, \text{rate}=\lambda)\), then
\[\begin{aligned} \P\{ S \in dt \} = \frac{\alpha^\lambda}{\Gamma(\alpha)} t^{\alpha - 1} e^{-\lambda t} dt . \end{aligned}\]
If \(T_1, \ldots, T_k\) are independent \(\Exp(\lambda)\), then \(S = T_1 + \cdots + T_k\) is \(\Gam(k, \lambda)\).
A machine produces \(n\) widgets per second; each widget has probability \(\lambda/n\) of being broken. The time until the \(k^\text{th}\) broken widget appears (in seconds) is approximately \(\sim \Gam(k, \lambda)\).
Back to baseball
The model
\[\begin{aligned} Z_i &\sim \Binom(N_i, \theta_i) \\ \theta_i &\sim \Beta(\mu_{p_i} \kappa_{p_i}, (1-\mu_{p_i})\kappa_{p_i}) \\ \mu &\sim \Beta(1, 1) \\ \kappa_p &\sim \Gam(0.1, 0.1) . \end{aligned}\]
pos_model <- "
data {
int N; // number of players
int hits[N];
int at_bats[N];
int npos; // number of positions
int position[N];
}
parameters {
real<lower=0, upper=1> theta[N];
real<lower=0, upper=1> mu[npos];
real<lower=0> kappa[npos];
}
model {
real alpha;
real beta;
hits ~ binomial(at_bats, theta);
for (i in 1:N) {
alpha = mu[position[i]] * kappa[position[i]];
beta = (1 - mu[position[i]]) * kappa[position[i]];
theta[i] ~ beta(alpha, beta);
}
mu ~ beta(1,1);
kappa ~ gamma(0.1,0.1);
}"batting <- read.csv("BattingAverage.csv", header=TRUE)
system.time(pos_fit <- stan(model_code=pos_model, chains=3, iter=100,
data=list(N=nrow(batting),
hits=batting$Hits,
at_bats=batting$AtBats,
npos=nlevels(batting$PriPos),
position=as.numeric(batting$PriPos))))## user system elapsed
## 83.672 0.968 68.372Diagnostics
## Inference for Stan model: db775bca82d7fc39d379745fb39b0819.
## 3 chains, each with iter=100; warmup=50; thin=1;
## post-warmup draws per chain=50, total post-warmup draws=150.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.25 0.00 0.01 0.24 0.25 0.25 0.26 0.26 150 1.00
## mu[2] 0.25 0.00 0.01 0.24 0.25 0.25 0.25 0.26 150 0.99
## mu[3] 0.26 0.00 0.01 0.24 0.25 0.25 0.26 0.27 102 1.03
## mu[4] 0.24 0.00 0.01 0.23 0.24 0.24 0.24 0.25 150 0.99
## mu[5] 0.26 0.00 0.01 0.25 0.25 0.26 0.26 0.27 150 1.00
## mu[6] 0.25 0.00 0.01 0.24 0.25 0.25 0.25 0.26 135 1.00
## mu[7] 0.13 0.00 0.01 0.12 0.13 0.13 0.13 0.14 49 1.02
## mu[8] 0.26 0.00 0.01 0.24 0.25 0.26 0.26 0.27 150 0.99
## mu[9] 0.25 0.00 0.01 0.23 0.24 0.25 0.25 0.26 150 0.99
## kappa[1] 114.88 2.30 26.14 71.55 97.48 111.02 129.46 171.96 129 1.02
## kappa[2] 106.91 2.10 25.73 64.27 86.57 106.71 123.82 166.11 150 1.01
## kappa[3] 98.36 2.13 18.60 67.26 85.47 97.46 109.55 139.78 76 1.03
## kappa[4] 95.51 1.87 20.90 59.52 81.30 92.11 107.85 136.19 125 0.99
## kappa[5] 99.94 1.96 19.88 64.93 83.72 100.08 112.14 142.69 103 1.02
## kappa[6] 104.78 1.91 19.86 69.61 90.25 104.28 116.12 148.35 108 1.00
## kappa[7] 54.50 2.25 10.81 35.97 46.05 53.83 62.41 76.05 23 1.10
## kappa[8] 121.88 2.41 29.57 73.44 102.79 119.24 139.14 184.28 150 1.00
## kappa[9] 93.11 2.94 23.34 58.17 76.77 90.33 108.38 144.98 63 1.02
##
## Samples were drawn using NUTS(diag_e) at Mon Nov 26 22:03:38 2018.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).Is it mixing?
Run longer!
system.time(pos_fit <- stan(model_code=pos_model, chains=3, iter=1000,
control=list(max_treedepth=15),
data=list(N=nrow(batting),
hits=batting$Hits,
at_bats=batting$AtBats,
npos=nlevels(batting$PriPos),
position=as.numeric(batting$PriPos))))## recompiling to avoid crashing R session## user system elapsed
## 1453.37 1.50 595.30## Inference for Stan model: db775bca82d7fc39d379745fb39b0819.
## 3 chains, each with iter=1000; warmup=500; thin=1;
## post-warmup draws per chain=500, total post-warmup draws=1500.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## mu[1] 0.25 0.00 0.01 0.24 0.25 0.25 0.26 0.26 1500 1.00
## mu[2] 0.25 0.00 0.01 0.24 0.24 0.25 0.25 0.26 1243 1.00
## mu[3] 0.26 0.00 0.01 0.24 0.25 0.26 0.26 0.27 1500 1.00
## mu[4] 0.24 0.00 0.01 0.23 0.24 0.24 0.24 0.25 1240 1.00
## mu[5] 0.26 0.00 0.01 0.24 0.25 0.26 0.26 0.27 1500 1.00
## mu[6] 0.25 0.00 0.01 0.24 0.25 0.25 0.25 0.26 1324 1.00
## mu[7] 0.13 0.00 0.01 0.12 0.13 0.13 0.13 0.14 528 1.01
## mu[8] 0.26 0.00 0.01 0.24 0.25 0.26 0.26 0.27 1500 1.00
## mu[9] 0.25 0.00 0.01 0.23 0.24 0.25 0.25 0.26 1500 1.00
## kappa[1] 111.28 0.72 22.73 71.99 95.06 109.19 124.41 162.22 1010 1.00
## kappa[2] 104.40 0.81 23.53 63.40 88.48 101.62 118.60 157.52 840 1.01
## kappa[3] 97.66 0.63 20.98 61.33 83.25 95.52 109.80 145.61 1109 1.00
## kappa[4] 95.48 0.74 19.70 62.44 81.45 94.06 107.42 137.05 714 1.01
## kappa[5] 102.00 0.69 21.93 65.47 85.96 100.75 115.39 151.21 1018 1.01
## kappa[6] 106.63 0.78 21.16 71.49 91.07 104.66 120.64 152.70 745 1.00
## kappa[7] 52.60 1.86 12.15 33.52 43.69 51.08 59.35 80.01 43 1.06
## kappa[8] 117.48 0.80 27.68 72.36 97.72 114.95 134.28 181.78 1207 1.00
## kappa[9] 93.55 0.69 22.33 56.79 78.05 91.18 106.90 142.96 1056 1.00
##
## Samples were drawn using NUTS(diag_e) at Mon Nov 26 22:13:36 2018.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).Is it mixing?
Let’s look at the results!
With labels: position means \(\mu_p\):
Position “concentrations”, \(\kappa_p\):
Simulation
Wouldn’t it be nice if we knew the truth?
Discuss:
Write down (on whiteboards) a procedure to simulate data that looks like the baseball data.
batting$post_mean <- colMeans(param_samples$theta)
batting$fake_hits <- rbinom(nrow(batting),
size=batting$AtBats,
prob=batting$post_mean)Option 1: By simulating draws from the posterior mean on \(\theta\), we can check that our model is accurately describing the data. Here is the real data against data simulated under the posterior mean \(\theta\) values. They look similar, which is good.
But if we want to know if we’re accurately estimating \(\mu\) and \(\kappa\), then we have to start with them, and simulate \(\theta\).
post_mean_mu <- colMeans(param_samples$mu)
post_mean_kappa <- colMeans(param_samples$kappa)
names(post_mean_mu) <- names(post_mean_kappa) <- levels(batting$PriPos)
batting$sim_theta <- rbeta(nrow(batting),
shape1=post_mean_mu[batting$PriPos] *
post_mean_kappa[batting$PriPos],
shape2=(1-post_mean_mu[batting$PriPos]) *
post_mean_kappa[batting$PriPos])
batting$sim_theta_hits <- rbinom(nrow(batting),
size=batting$AtBats,
prob=batting$sim_theta)Fit the model to the simulated data:
sim_fit <- stan(model_code=pos_model, chains=3, iter=1000, control=list(max_treedepth=13),
data=list(N=nrow(batting),
hits=batting$sim_theta_hits,
at_bats=batting$AtBats,
npos=nlevels(batting$PriPos),
position=as.numeric(batting$PriPos)))## recompiling to avoid crashing R sessionCan we estimate \(\mu\) and \(\kappa\)?
sim_samples <- extract(sim_fit)
layout(t(1:2))
boxplot(sim_samples$mu, main="posterior distribution of mu")
points(1:9, post_mean_mu, col='red', pch=20, cex=2)
boxplot(sim_samples$kappa, main="posterior distribution of kappa")
points(1:9, post_mean_kappa, col='red', pch=20, cex=2)
General questions with simulated data
- Does my statistical inference method work?
Do the credible intervals contain the true value?
(i.e., Is the method “well-calibrated”?)
They usually should.
How wide are credible intervals, typically?
This is (one kind of) statistical power.
Posterior predictive sampling
How to choose parameter values for simulation?
It depends, but one good choice is from the posterior distribution - then you can see how the model behaves with data close to the real data.
This is known as posterior predictive sampling.
Sharing power // Shrinkage
Example
Suppose that I have a large pot of coins that are all similar to each other. I flip each one ten times, and record the number of Heads. What is each coin’s probability of Heads?
Treated separately, we would be very uncertain about each coin.
Together, they should tell us very accurately what are likely values of \(\theta\).
This information can improve the estimate of each separate \(\theta\).
The more similar the coins are, the more information we gain.
Shrinkage and baseball
Some players were at bat very few times. How does the information about their position affect our inference about their batting averages?
batting$post_med <- colMedians(param_samples$theta)
batting$post_Q1 <- colQuantiles(param_samples$theta, probs=0.25)
batting$post_Q3 <- colQuantiles(param_samples$theta, probs=0.75)
pos_means <- colMeans(param_samples$mu)
names(pos_means) <- levels(batting$PriPos)
pos_means## 1st Base 2nd Base 3rd Base Catcher Center Field
## 0.2524128 0.2488493 0.2555532 0.2392593 0.2582094
## Left Field Pitcher Right Field Shortstop
## 0.2491433 0.1290069 0.2584937 0.2473966Pitchers had posterior mean \(\mu\) of 0.1290069
with(subset(batting[order(batting$post_med),], PriPos=="Pitcher"), {
plot(Hits / AtBats, main="Pitchers", xaxt='n', ylim=c(0, 0.4),
xlab='player', ylab="posterior median theta");
segments(x0=seq_along(Hits), y0=post_Q1, y1=post_Q3,
col=adjustcolor('red',0.5));
points(post_med, pch=20) })
abline(h=pos_means["Pitcher"], lwd=2, col=adjustcolor("blue", 0.5))
Catchers had posterior mean \(\mu\) of 0.2392593
with(subset(batting[order(batting$post_med),], PriPos=="Catcher"), {
plot(Hits / AtBats, main="Catchers", xaxt='n', ylim=c(0, 0.4),
xlab='player', ylab="posterior median theta");
segments(x0=seq_along(Hits), y0=post_Q1, y1=post_Q3,
col=adjustcolor('red',0.5));
points(post_med, pch=20) })
abline(h=pos_means["Catcher"], lwd=2, col=adjustcolor("blue", 0.5))
Is shrinkage here a good idea?
With simulated data, compare median absolute error for
posterior mean \(\theta_i\)
empirical batting average
How’d we do? Let’s look at the true values of \(\theta\) (we know because we generated them) against the posterior means. Red lines are 95% credible intervals.
post_sim_theta <- colMeans(sim_samples$theta)
plot(batting$sim_theta, post_sim_theta, type='n', xlab="true theta", ylab="posterior mean theta", ylim=c(0,0.4))
segments(x0=batting$sim_theta, col='red',
y0=colQuantiles(sim_samples$theta, probs=0.05),
y1=colQuantiles(sim_samples$theta, probs=0.95))
points(batting$sim_theta, post_sim_theta, pch=20)
abline(0, 1, lwd=3, col=adjustcolor('blue', 0.5))
Did we do better?
The mean absolute difference between the truth and
- posterior mean: 0.0255297
- empirical batting average (hits/at bats): 0.0862214
Using information about groups reduced our error by a factor of 4!
Logistic regression, a.k.a. metric predictors
Motivation
There’s a good bit more information available about the baseball players.
## Player PriPos Hits AtBats PlayerNumber PriPosNumber
## 1 Aaron Cunningham Left Field 17 97 198 7
## 2 Aaron Harang Pitcher 4 56 360 1
## 3 Aaron Hill 2nd Base 184 609 394 4
## 4 Aaron Laffey Pitcher 0 1 482 1
## 5 Aaron Loup Pitcher 0 1 522 1
## 6 Adam Dunn 1st Base 110 539 242 3
## playerID weight height bats birthYear debut finalGame
## 1 cunniaa01 215 71 R 1986 2008-08-31 2012-07-24
## 2 haranaa01 260 79 R 1978 2002-05-25 2015-10-03
## 3 hillaa01 200 71 R 1982 2005-05-20 2016-10-01
## 4 laffeaa01 190 71 L 1985 2007-08-04 2015-07-31
## 5 loupaa01 210 71 L 1987 2012-07-14 2016-09-30
## 6 dunnad01 285 78 L 1979 2001-07-20 2014-09-28Is batting average predicted by weight and height?
Each player has their own batting avg, \(\theta_i\).
Batting averages tend to be different for different positions.
After accounting for position (\(p_i\)), \(\theta\) varies with height (\(h_i\)) and/or weight (\(w_i\)).
\[\begin{aligned} Z_i &\sim \Binom(N_i, \theta_i) \\ \theta_i &= \Beta(\mu_i \kappa_{p_i}, (1-\mu_i) \kappa_{p_i}) \\ \mu_i &= \logistic(\gamma_{p_i} + \alpha_h h_i + \alpha_w w_i) \\ \kappa_p &\sim \Gam(0.1, 0.1) \\ \gamma_{p} &\sim \Normal(0, \sigma_\gamma) \\ \alpha_h &\sim \Normal(0, \sigma_h) \\ \alpha_w &\sim \Normal(0, \sigma_w) \\ \sigma_\gamma, \sigma_h, \sigma_w &\sim \Normal^+(0, 20) \end{aligned}\]
Stan
logistic_model <- "
data {
int N; // number of players
int hits[N];
int at_bats[N];
int npos; // number of positions
int position[N];
vector[N] height;
vector[N] weight;
}
parameters {
real<lower=0, upper=1> theta[N];
vector[npos] gamma;
real alpha_w;
real alpha_h;
vector<lower=0>[npos] kappa;
}
model {
vector[N] mu;
mu = inv_logit(gamma[position] + alpha_h * height + alpha_w * weight);
theta ~ beta(mu .* kappa[position], (1-mu) .* kappa[position]);
hits ~ binomial(at_bats, theta);
kappa ~ gamma(0.1, 0.1);
gamma ~ normal(0, 5);
alpha_h ~ normal(0, 5);
alpha_w ~ normal(0, 5);
} "\[\begin{aligned} Z_i &\sim \Binom(N_i, \theta_i) \\ \theta_i &= \Beta(\mu_i \kappa_{p_i}, (1-\mu_i) \kappa_{p_i}) \\ \mu_i &= \logistic(\gamma_{p_i} + \alpha_h h_i + \alpha_w w_i) \\ \kappa_p &\sim \Gam(0.1, 0.1) \\ \gamma_{p} &\sim \Normal(0, 5) \\ \alpha_h &\sim \Normal(0, 5) \\ \alpha_w &\sim \Normal(0, 5) \end{aligned}\]
New features
logistic_model <- "
data {
int N; // number of players
int hits[N];
int at_bats[N];
int npos; // number of positions
int position[N];
vector[N] height;
vector[N] weight;
}
parameters {
real<lower=0, upper=1> theta[N];
vector[npos] gamma;
real alpha_w;
real alpha_h;
vector<lower=0>[npos] kappa;
}
model {
vector[N] mu;
mu = inv_logit(gamma[position] + alpha_h * height + alpha_w * weight);
theta ~ beta(mu .* kappa[position], (1-mu) .* kappa[position]);
hits ~ binomial(at_bats, theta);
kappa ~ gamma(0.1, 0.1);
gamma ~ normal(0, 5);
alpha_h ~ normal(0, 5);
alpha_w ~ normal(0, 5);
} "vector[N] height;instead ofreal height[N];: to allowalpha_h * height.we will center and scale height and weight before passing to Stan
x .* yfor component-wise multiplication
data {
int N; // number of players
int hits[N];
int at_bats[N];
int npos; // number of positions
int position[N];
vector[N] height;
vector[N] weight;
}
parameters {
real<lower=0, upper=1> theta[N];
vector[npos] gamma;
real alpha_w;
real alpha_h;
vector<lower=0>[npos] kappa;
}
model {
vector[N] mu;
mu = inv_logit(gamma[position] + alpha_h * height + alpha_w * weight);
theta ~ beta(mu .* kappa[position], (1-mu) .* kappa[position]);
hits ~ binomial(at_bats, theta);
kappa ~ gamma(0.1, 0.1);
gamma ~ normal(0, 5);
alpha_h ~ normal(0, 5);
alpha_w ~ normal(0, 5);
} scaled_height <- (batplus$height - mean(batplus$height))/sd(batplus$height)
scaled_weight <- (batplus$weight - mean(batplus$weight))/sd(batplus$weight)
system.time(logistic_fit <- stan(model_code=logistic_model, chains=3, iter=1000,
control=list(adapt_delta=0.9, max_treedepth=12),
data=list(N=nrow(batplus),
hits=batplus$Hits,
at_bats=batplus$AtBats,
npos=nlevels(batplus$PriPos),
position=as.numeric(batplus$PriPos),
height=scaled_height,
weight=scaled_weight) ))## user system elapsed
## 416.875 1.121 174.229## mean se_mean sd 2.5%
## theta[1] 2.154388e-01 0.0007513784 0.02910076 1.613308e-01
## theta[2] 1.010041e-01 0.0007535651 0.02918545 4.941614e-02
## theta[3] 2.951447e-01 0.0004623617 0.01790719 2.602717e-01
## theta[4] 1.254564e-01 0.0011644361 0.04509842 5.304982e-02
## theta[5] 1.267264e-01 0.0011760042 0.04554644 4.899489e-02
## theta[6] 2.137332e-01 0.0004372399 0.01693423 1.809926e-01
## theta[7] 2.839817e-01 0.0004257675 0.01648990 2.522482e-01
## theta[8] 2.595476e-01 0.0007075845 0.02740463 2.067130e-01
## theta[9] 2.685346e-01 0.0004560665 0.01766338 2.345357e-01
## theta[10] 2.536820e-01 0.0005363106 0.02077122 2.132758e-01
## theta[11] 2.312560e-01 0.0010999148 0.04259952 1.517031e-01
## theta[12] 1.259490e-01 0.0010568977 0.04093347 5.621182e-02
## theta[13] 2.360344e-01 0.0007676425 0.02973066 1.813286e-01
## theta[14] 1.254595e-01 0.0008011102 0.03102686 7.316394e-02
## theta[15] 2.537381e-01 0.0007365677 0.02852714 2.000469e-01
## theta[16] 3.130492e-01 0.0004554680 0.01764020 2.786606e-01
## theta[17] 2.250474e-01 0.0008772269 0.03397485 1.610216e-01
## theta[18] 2.922307e-01 0.0004048141 0.01567838 2.624320e-01
## theta[19] 2.461626e-01 0.0009017036 0.03492283 1.824965e-01
## theta[20] 2.804723e-01 0.0004195641 0.01624965 2.496350e-01
## theta[21] 2.538730e-01 0.0004698431 0.01819694 2.167503e-01
## theta[22] 2.465243e-01 0.0009897220 0.03833177 1.755113e-01
## theta[23] 2.861012e-01 0.0004370176 0.01692562 2.538393e-01
## theta[24] 2.772517e-01 0.0004659201 0.01804501 2.431177e-01
## theta[25] 2.417227e-01 0.0005047359 0.01954834 2.036217e-01
## theta[26] 2.347186e-01 0.0009699454 0.03756582 1.661172e-01
## theta[27] 2.887455e-01 0.0004053230 0.01569809 2.575464e-01
## theta[28] 1.231131e-01 0.0010963976 0.04246330 5.457509e-02
## theta[29] 2.386940e-01 0.0007241413 0.02804587 1.859416e-01
## theta[30] 2.390084e-01 0.0005289159 0.02048483 2.008726e-01
## theta[31] 2.964546e-01 0.0004424148 0.01713465 2.634389e-01
## theta[32] 2.695385e-01 0.0004798559 0.01858474 2.352759e-01
## theta[33] 1.476297e-01 0.0009574322 0.03708119 8.281407e-02
## theta[34] 2.619096e-01 0.0004079012 0.01579795 2.312427e-01
## theta[35] 2.414780e-01 0.0005469429 0.02118301 2.021519e-01
## theta[36] 2.423402e-01 0.0005676652 0.02198558 1.995845e-01
## theta[37] 1.435681e-01 0.0012402257 0.04803374 6.371318e-02
## theta[38] 2.599975e-01 0.0004445634 0.01721787 2.277619e-01
## theta[39] 1.227799e-01 0.0011211251 0.04342099 4.931790e-02
## theta[40] 2.248427e-01 0.0011333814 0.04389567 1.436920e-01
## theta[41] 2.966284e-01 0.0005202765 0.02015022 2.586743e-01
## theta[42] 2.797881e-01 0.0004522460 0.01751541 2.468103e-01
## theta[43] 2.741723e-01 0.0007285862 0.02821802 2.215140e-01
## theta[44] 2.361440e-01 0.0005037074 0.01950851 1.977580e-01
## theta[45] 1.307717e-01 0.0011331323 0.04388602 5.835735e-02
## theta[46] 3.180680e-01 0.0004316743 0.01671867 2.866312e-01
## theta[47] 2.770905e-01 0.0011990440 0.04643877 1.928315e-01
## theta[48] 1.216318e-01 0.0010860819 0.04206377 5.157456e-02
## theta[49] 2.139168e-01 0.0005868199 0.02272744 1.708604e-01
## theta[50] 3.028769e-01 0.0005810228 0.02250292 2.602865e-01
## theta[51] 2.232699e-01 0.0007493583 0.02902252 1.692382e-01
## theta[52] 1.393534e-01 0.0012318924 0.04771099 6.055820e-02
## theta[53] 1.510008e-01 0.0012885937 0.04990702 6.692156e-02
## theta[54] 2.834543e-01 0.0004525753 0.01752816 2.488340e-01
## theta[55] 1.188279e-01 0.0009513861 0.03684702 5.595375e-02
## theta[56] 1.282518e-01 0.0009757127 0.03778919 6.157004e-02
## theta[57] 2.353969e-01 0.0006377658 0.02470056 1.893113e-01
## theta[58] 2.070441e-01 0.0009033703 0.03498738 1.412725e-01
## theta[59] 2.777324e-01 0.0005492726 0.02127323 2.390679e-01
## theta[60] 1.237152e-01 0.0012075248 0.04676723 4.609723e-02
## theta[61] 2.935257e-01 0.0004640365 0.01797206 2.577131e-01
## theta[62] 1.125571e-01 0.0010711754 0.04148644 4.389257e-02
## theta[63] 2.673478e-01 0.0004650433 0.01801105 2.329516e-01
## theta[64] 2.268801e-01 0.0008455107 0.03274649 1.617163e-01
## theta[65] 2.942908e-01 0.0004792004 0.01855935 2.591605e-01
## theta[66] 2.481085e-01 0.0007332727 0.02839953 1.938546e-01
## theta[67] 2.787744e-01 0.0009508985 0.03682814 2.093714e-01
## theta[68] 1.280215e-01 0.0011677792 0.04522789 5.219603e-02
## theta[69] 1.012467e-01 0.0007266672 0.02814370 5.258416e-02
## theta[70] 1.290357e-01 0.0011480744 0.04446473 5.450379e-02
## theta[71] 2.447316e-01 0.0006385312 0.02473021 2.000202e-01
## theta[72] 2.867547e-01 0.0004611743 0.01786120 2.525090e-01
## theta[73] 1.016773e-01 0.0009815476 0.03801517 3.736270e-02
## theta[74] 2.684131e-01 0.0004379131 0.01696030 2.363957e-01
## theta[75] 3.050106e-01 0.0004709926 0.01824147 2.703829e-01
## theta[76] 1.263261e-01 0.0011110127 0.04302934 5.395910e-02
## theta[77] 2.249351e-01 0.0009395147 0.03638725 1.543327e-01
## theta[78] 2.225328e-01 0.0010980126 0.04252585 1.435075e-01
## theta[79] 2.314720e-01 0.0009892565 0.03831374 1.599119e-01
## theta[80] 2.454088e-01 0.0006393897 0.02476346 1.956020e-01
## theta[81] 2.215010e-01 0.0006953022 0.02692894 1.701993e-01
## theta[82] 1.282643e-01 0.0012075779 0.04676929 5.129379e-02
## theta[83] 1.274553e-01 0.0012063403 0.04672136 5.274079e-02
## theta[84] 1.279078e-01 0.0012375070 0.04792844 4.806390e-02
## theta[85] 1.438391e-01 0.0011202992 0.04338900 7.168052e-02
## theta[86] 1.322846e-01 0.0012462499 0.04826705 5.328147e-02
## theta[87] 1.403734e-01 0.0012510736 0.04845387 5.832236e-02
## theta[88] 2.295426e-01 0.0009771258 0.03784392 1.586348e-01
## theta[89] 2.301295e-01 0.0007812673 0.03025835 1.721087e-01
## theta[90] 1.484311e-01 0.0010562779 0.04090947 8.092326e-02
## theta[91] 2.699595e-01 0.0004882704 0.01891063 2.310295e-01
## theta[92] 2.485012e-01 0.0004867419 0.01885143 2.126226e-01
## theta[93] 1.412422e-01 0.0012173292 0.04714696 6.192501e-02
## theta[94] 1.272150e-01 0.0012202057 0.04725836 5.055709e-02
## theta[95] 2.391933e-01 0.0010590746 0.04101778 1.606312e-01
## theta[96] 2.170339e-01 0.0009095633 0.03522723 1.520260e-01
## theta[97] 2.271316e-01 0.0005500507 0.02130337 1.866004e-01
## theta[98] 2.565684e-01 0.0009840875 0.03811355 1.870403e-01
## theta[99] 2.791356e-01 0.0006711249 0.02599256 2.292329e-01
## theta[100] 2.767538e-01 0.0004349339 0.01684492 2.449400e-01
## theta[101] 2.614496e-01 0.0008749814 0.03388788 1.978545e-01
## theta[102] 2.384232e-01 0.0006367584 0.02466155 1.912339e-01
## theta[103] 2.034882e-01 0.0004545393 0.01760423 1.700918e-01
## theta[104] 2.440980e-01 0.0004819489 0.01866580 2.082459e-01
## theta[105] 2.140118e-01 0.0005767277 0.02233657 1.718426e-01
## theta[106] 2.146120e-01 0.0007578841 0.02935273 1.596675e-01
## theta[107] 2.547714e-01 0.0011845246 0.04587644 1.693486e-01
## theta[108] 1.270211e-01 0.0011609361 0.04496286 5.306787e-02
## theta[109] 2.643775e-01 0.0009669270 0.03744892 1.973854e-01
## theta[110] 2.173300e-01 0.0007564153 0.02929584 1.606694e-01
## theta[111] 2.116679e-01 0.0007068000 0.02737425 1.626611e-01
## theta[112] 2.711027e-01 0.0004813825 0.01864386 2.362973e-01
## theta[113] 2.311396e-01 0.0007573768 0.02933308 1.765753e-01
## theta[114] 2.544458e-01 0.0005869384 0.02273203 2.126670e-01
## theta[115] 2.276390e-01 0.0008140107 0.03152650 1.679011e-01
## theta[116] 2.159664e-01 0.0004919922 0.01905477 1.786343e-01
## theta[117] 2.374817e-01 0.0005256788 0.02035945 1.984175e-01
## theta[118] 1.271283e-01 0.0012284696 0.04757842 4.940784e-02
## theta[119] 1.344556e-01 0.0011861158 0.04593807 5.932001e-02
## theta[120] 2.312583e-01 0.0004799523 0.01858847 1.971929e-01
## theta[121] 2.217526e-01 0.0008545767 0.03309761 1.598776e-01
## theta[122] 1.247372e-01 0.0012489862 0.04837303 4.600157e-02
## theta[123] 2.304759e-01 0.0008325722 0.03224538 1.683637e-01
## theta[124] 2.668190e-01 0.0008719214 0.03376937 2.016103e-01
## theta[125] 1.367415e-01 0.0008883108 0.03440413 7.645866e-02
## theta[126] 1.931282e-01 0.0007523472 0.02913828 1.365435e-01
## theta[127] 1.384411e-01 0.0011189442 0.04333652 6.594014e-02
## theta[128] 1.380850e-01 0.0011294162 0.04374210 6.488018e-02
## theta[129] 2.379567e-01 0.0011608144 0.04495815 1.545574e-01
## theta[130] 2.396956e-01 0.0011497411 0.04452928 1.573790e-01
## theta[131] 2.577904e-01 0.0005434369 0.02104722 2.183731e-01
## theta[132] 2.113792e-01 0.0005670411 0.02196141 1.699525e-01
## theta[133] 2.689161e-01 0.0004575529 0.01772095 2.355632e-01
## theta[134] 1.153613e-01 0.0008193519 0.03173336 5.980600e-02
## theta[135] 1.248141e-01 0.0012736612 0.04932869 4.962135e-02
## theta[136] 3.218109e-01 0.0004969856 0.01924817 2.850850e-01
## theta[137] 2.453602e-01 0.0004402970 0.01705263 2.140738e-01
## theta[138] 2.674372e-01 0.0007921033 0.03067803 2.092095e-01
## theta[139] 1.280447e-01 0.0011635372 0.04506360 5.292316e-02
## theta[140] 2.666179e-01 0.0004686348 0.01815015 2.313486e-01
## theta[141] 2.545409e-01 0.0008616525 0.03337166 1.960098e-01
## theta[142] 2.600347e-01 0.0005089568 0.01971181 2.242079e-01
## theta[143] 2.945002e-01 0.0004661547 0.01805409 2.588900e-01
## theta[144] 2.632471e-01 0.0004438141 0.01718885 2.300254e-01
## theta[145] 2.345201e-01 0.0008528371 0.03303024 1.712820e-01
## theta[146] 2.075196e-01 0.0004329754 0.01676906 1.775117e-01
## theta[147] 2.587131e-01 0.0005498910 0.02129719 2.188061e-01
## theta[148] 3.088668e-01 0.0005549052 0.02149139 2.690157e-01
## theta[149] 2.506114e-01 0.0004615623 0.01787623 2.173665e-01
## theta[150] 1.403670e-01 0.0011559218 0.04476866 6.646060e-02
## theta[151] 2.422177e-01 0.0011007973 0.04263370 1.613883e-01
## theta[152] 1.440907e-01 0.0012405234 0.04804527 6.389947e-02
## theta[153] 1.514484e-01 0.0010270515 0.03977753 8.562307e-02
## theta[154] 1.388912e-01 0.0012889000 0.04991888 5.820844e-02
## theta[155] 1.415773e-01 0.0011741945 0.04547636 6.776618e-02
## theta[156] 2.335040e-01 0.0004432059 0.01716529 2.015861e-01
## theta[157] 2.262962e-01 0.0005342770 0.02069246 1.867724e-01
## theta[158] 2.335998e-01 0.0005464505 0.02116394 1.928099e-01
## theta[159] 1.245289e-01 0.0011215669 0.04343810 5.213245e-02
## theta[160] 2.433962e-01 0.0006946288 0.02690286 1.935350e-01
## theta[161] 1.251184e-01 0.0011487485 0.04449084 4.991346e-02
## theta[162] 1.595440e-01 0.0010045073 0.03890440 9.099275e-02
## theta[163] 1.119101e-01 0.0010599750 0.04105266 4.306097e-02
## theta[164] 2.598135e-01 0.0008121036 0.03145264 2.002191e-01
## theta[165] 2.702167e-01 0.0007703725 0.02983640 2.140751e-01
## theta[166] 2.291512e-01 0.0010006017 0.03875314 1.580292e-01
## theta[167] 2.824605e-01 0.0004229620 0.01638125 2.511582e-01
## theta[168] 2.534291e-01 0.0005580572 0.02161346 2.120688e-01
## theta[169] 2.804574e-01 0.0005672474 0.02196940 2.397971e-01
## theta[170] 2.061444e-01 0.0006378610 0.02470425 1.604378e-01
## theta[171] 1.203657e-01 0.0011278750 0.04368241 4.947426e-02
## theta[172] 1.103351e-01 0.0007764286 0.03007095 6.058167e-02
## theta[173] 1.960079e-01 0.0007816329 0.03027251 1.373278e-01
## theta[174] 2.674624e-01 0.0004222014 0.01635179 2.358314e-01
## theta[175] 2.845997e-01 0.0005433141 0.02104247 2.434618e-01
## theta[176] 2.535064e-01 0.0010457200 0.04050056 1.786467e-01
## theta[177] 2.657585e-01 0.0007024576 0.02720606 2.182313e-01
## theta[178] 2.514749e-01 0.0008257826 0.03198242 1.910164e-01
## theta[179] 2.624281e-01 0.0005364460 0.02077646 2.222972e-01
## theta[180] 2.057120e-01 0.0010328012 0.04000022 1.335095e-01
## theta[181] 2.395509e-01 0.0006128055 0.02373385 1.950576e-01
## theta[182] 2.772709e-01 0.0004730722 0.01832201 2.428659e-01
## theta[183] 1.263829e-01 0.0012375671 0.04793077 4.789995e-02
## theta[184] 1.206719e-01 0.0011221289 0.04345987 4.947159e-02
## theta[185] 2.913773e-01 0.0005534058 0.02143331 2.502265e-01
## theta[186] 2.377866e-01 0.0006634609 0.02569573 1.881152e-01
## theta[187] 1.216361e-01 0.0011898271 0.04608181 4.495284e-02
## theta[188] 1.358999e-01 0.0011101652 0.04299651 6.381878e-02
## theta[189] 1.205975e-01 0.0011435115 0.04428801 4.409627e-02
## theta[190] 1.381236e-01 0.0012067147 0.04673586 6.328958e-02
## theta[191] 1.949018e-01 0.0005861582 0.02270181 1.522963e-01
## theta[192] 2.386773e-01 0.0007239863 0.02803987 1.858786e-01
## theta[193] 1.459876e-01 0.0010114446 0.03917308 8.002258e-02
## theta[194] 1.125292e-01 0.0009197659 0.03562238 5.024586e-02
## theta[195] 1.219654e-01 0.0012449678 0.04821740 4.635759e-02
## theta[196] 1.275752e-01 0.0011657115 0.04514781 5.194149e-02
## theta[197] 1.703322e-01 0.0009279496 0.03593934 1.043281e-01
## theta[198] 1.234445e-01 0.0012587959 0.04875296 4.428716e-02
## theta[199] 1.054778e-01 0.0007286129 0.02821906 5.626439e-02
## theta[200] 2.344128e-01 0.0009874077 0.03824214 1.609153e-01
## theta[201] 2.211952e-01 0.0004627244 0.01792124 1.873930e-01
## theta[202] 2.321749e-01 0.0004666377 0.01807280 1.967378e-01
## theta[203] 2.587015e-01 0.0004706778 0.01822927 2.250276e-01
## theta[204] 2.266977e-01 0.0005967304 0.02311127 1.824814e-01
## theta[205] 2.646246e-01 0.0004618607 0.01788779 2.302318e-01
## theta[206] 1.580595e-01 0.0013356274 0.05172863 6.964435e-02
## theta[207] 2.280378e-01 0.0004226669 0.01636982 1.965157e-01
## theta[208] 1.783943e-01 0.0008731547 0.03381714 1.179697e-01
## theta[209] 2.577580e-01 0.0008076430 0.03127988 1.999197e-01
## theta[210] 1.181640e-01 0.0011560264 0.04477271 4.600580e-02
## theta[211] 2.348334e-01 0.0010457384 0.04050127 1.600140e-01
## theta[212] 2.412794e-01 0.0009522537 0.03688063 1.750939e-01
## theta[213] 2.369239e-01 0.0009306772 0.03604497 1.727086e-01
## theta[214] 2.668735e-01 0.0004448493 0.01722894 2.336191e-01
## theta[215] 1.268172e-01 0.0011613532 0.04497902 5.247063e-02
## theta[216] 1.049945e-01 0.0010206672 0.03953027 3.771738e-02
## theta[217] 1.225911e-01 0.0011803445 0.04571455 5.081346e-02
## theta[218] 2.902128e-01 0.0006708361 0.02598137 2.405814e-01
## theta[219] 1.165602e-01 0.0011029086 0.04271547 4.369423e-02
## theta[220] 1.214895e-01 0.0011481103 0.04446612 4.955704e-02
## theta[221] 2.350991e-01 0.0004256008 0.01648345 2.035935e-01
## theta[222] 1.263206e-01 0.0011841173 0.04586067 5.000892e-02
## theta[223] 1.211903e-01 0.0010261688 0.03974335 5.390326e-02
## theta[224] 1.187816e-01 0.0012005636 0.04649763 4.270078e-02
## theta[225] 1.267655e-01 0.0012368185 0.04790178 5.249915e-02
## theta[226] 2.712046e-01 0.0010226045 0.03960530 2.001091e-01
## theta[227] 1.265107e-01 0.0011983227 0.04641084 5.091672e-02
## theta[228] 2.250917e-01 0.0004340667 0.01681133 1.942277e-01
## theta[229] 1.238741e-01 0.0011592732 0.04489846 4.752564e-02
## theta[230] 2.326201e-01 0.0004976355 0.01927334 1.971002e-01
## theta[231] 1.357993e-01 0.0010862467 0.04207016 6.682576e-02
## theta[232] 2.848366e-01 0.0004697606 0.01819375 2.504710e-01
## theta[233] 2.439913e-01 0.0005852972 0.02266846 2.010077e-01
## theta[234] 2.479338e-01 0.0004426873 0.01714520 2.145915e-01
## theta[235] 2.142029e-01 0.0006641197 0.02572125 1.644802e-01
## theta[236] 2.338564e-01 0.0008377811 0.03244712 1.729335e-01
## theta[237] 2.278868e-01 0.0007294895 0.02825301 1.753785e-01
## theta[238] 2.531948e-01 0.0006628751 0.02567304 2.038525e-01
## theta[239] 2.737194e-01 0.0009963666 0.03858911 2.028188e-01
## theta[240] 2.286173e-01 0.0007499205 0.02904430 1.748941e-01
## theta[241] 2.527701e-01 0.0004455669 0.01725673 2.198475e-01
## theta[242] 2.642903e-01 0.0008386108 0.03247926 2.021850e-01
## theta[243] 2.792189e-01 0.0007379510 0.02858072 2.262233e-01
## theta[244] 2.616447e-01 0.0004648652 0.01800415 2.258957e-01
## theta[245] 2.878257e-01 0.0004776351 0.01849873 2.513620e-01
## theta[246] 1.498258e-01 0.0013159256 0.05096558 6.810547e-02
## theta[247] 1.252880e-01 0.0011588466 0.04488193 5.129872e-02
## theta[248] 2.485096e-01 0.0009121139 0.03532602 1.798895e-01
## theta[249] 2.936943e-01 0.0004968604 0.01924332 2.576892e-01
## theta[250] 3.021279e-01 0.0005834576 0.02259722 2.580115e-01
## theta[251] 1.187827e-01 0.0010925931 0.04231595 4.627846e-02
## theta[252] 2.509552e-01 0.0007037182 0.02725489 1.989009e-01
## theta[253] 2.992697e-01 0.0004414074 0.01709564 2.674893e-01
## theta[254] 2.559867e-01 0.0004495902 0.01741255 2.219422e-01
## theta[255] 2.317611e-01 0.0005577322 0.02160088 1.897998e-01
## theta[256] 2.649526e-01 0.0004318434 0.01672522 2.323622e-01
## theta[257] 2.798657e-01 0.0004747303 0.01838623 2.430477e-01
## theta[258] 2.656066e-01 0.0012019471 0.04655121 1.803940e-01
## theta[259] 1.230956e-01 0.0011761963 0.04555389 5.105121e-02
## theta[260] 3.081305e-01 0.0004262832 0.01650988 2.772357e-01
## theta[261] 1.560675e-01 0.0012869509 0.04984340 6.856792e-02
## theta[262] 2.124793e-01 0.0006287543 0.02435155 1.655405e-01
## theta[263] 2.455626e-01 0.0004589302 0.01777429 2.127278e-01
## theta[264] 2.215149e-01 0.0006345286 0.02457519 1.746807e-01
## theta[265] 2.553092e-01 0.0005947124 0.02303311 2.106860e-01
## theta[266] 2.919011e-01 0.0005354078 0.02073626 2.511889e-01
## theta[267] 2.571871e-01 0.0010867029 0.04208782 1.814011e-01
## theta[268] 1.368236e-01 0.0010091497 0.03908420 6.871274e-02
## theta[269] 2.615714e-01 0.0008769182 0.03396289 1.998166e-01
## theta[270] 2.818553e-01 0.0006353807 0.02460819 2.313333e-01
## theta[271] 2.438978e-01 0.0006657278 0.02578353 1.924732e-01
## theta[272] 2.205965e-01 0.0007367259 0.02853327 1.683258e-01
## theta[273] 2.335146e-01 0.0007797054 0.03019786 1.759506e-01
## theta[274] 2.832698e-01 0.0006032432 0.02336351 2.386024e-01
## theta[275] 1.226837e-01 0.0011896809 0.04607614 4.851441e-02
## theta[276] 2.146403e-01 0.0007384905 0.02860161 1.604850e-01
## theta[277] 1.236806e-01 0.0011459056 0.04438073 5.177524e-02
## theta[278] 1.644594e-01 0.0010335577 0.04002952 9.437309e-02
## theta[279] 1.246335e-01 0.0012299248 0.04763478 4.654978e-02
## theta[280] 2.197656e-01 0.0004451441 0.01724036 1.868357e-01
## theta[281] 2.508386e-01 0.0007258513 0.02811210 1.995853e-01
## theta[282] 1.259021e-01 0.0012777208 0.04948591 4.402489e-02
## theta[283] 2.290834e-01 0.0004078325 0.01579529 1.991865e-01
## theta[284] 1.271547e-01 0.0012199185 0.04724724 4.913002e-02
## theta[285] 2.829084e-01 0.0004543258 0.01759596 2.500000e-01
## theta[286] 1.003364e-01 0.0007449610 0.02885222 5.068912e-02
## theta[287] 2.297367e-01 0.0007038463 0.02725985 1.783802e-01
## theta[288] 2.704252e-01 0.0008436480 0.03267435 2.109878e-01
## theta[289] 1.273903e-01 0.0012189029 0.04720791 4.901086e-02
## theta[290] 2.762081e-01 0.0004439435 0.01719386 2.432996e-01
## theta[291] 1.806211e-01 0.0009392817 0.03637823 1.153872e-01
## theta[292] 2.473593e-01 0.0009115311 0.03530345 1.809087e-01
## theta[293] 2.212163e-01 0.0010680514 0.04136545 1.456740e-01
## theta[294] 2.506088e-01 0.0006426445 0.02488951 2.031211e-01
## theta[295] 2.430340e-01 0.0005972607 0.02313181 1.988818e-01
## theta[296] 1.272216e-01 0.0012049419 0.04666720 5.314132e-02
## theta[297] 2.814642e-01 0.0004458939 0.01726940 2.490497e-01
## theta[298] 2.589736e-01 0.0006082070 0.02355575 2.142247e-01
## theta[299] 2.275802e-01 0.0006774480 0.02623745 1.789516e-01
## theta[300] 2.189454e-01 0.0006600209 0.02556250 1.709204e-01
## theta[301] 2.748517e-01 0.0006121095 0.02370690 2.287686e-01
## theta[302] 2.390976e-01 0.0011082818 0.04292357 1.565695e-01
## theta[303] 2.486432e-01 0.0010879101 0.04213458 1.703174e-01
## theta[304] 1.245699e-01 0.0011293822 0.04374078 5.153285e-02
## theta[305] 2.230634e-01 0.0006769533 0.02621829 1.748292e-01
## theta[306] 2.356400e-01 0.0004252432 0.01646960 2.046341e-01
## theta[307] 2.031855e-01 0.0007764266 0.03007087 1.469994e-01
## theta[308] 1.710350e-01 0.0010461584 0.04051754 1.001146e-01
## theta[309] 2.365896e-01 0.0005823928 0.02255598 1.932076e-01
## theta[310] 2.840514e-01 0.0004671280 0.01809179 2.492799e-01
## theta[311] 1.197366e-01 0.0008351702 0.03234600 6.474310e-02
## theta[312] 2.422647e-01 0.0008637115 0.03345140 1.787949e-01
## theta[313] 2.454665e-01 0.0007398666 0.02865491 1.916203e-01
## theta[314] 1.169828e-01 0.0010938841 0.04236595 4.693224e-02
## theta[315] 1.404676e-01 0.0012090288 0.04682549 6.282547e-02
## theta[316] 2.552319e-01 0.0012081847 0.04679279 1.682021e-01
## theta[317] 2.807542e-01 0.0005960628 0.02308541 2.341331e-01
## theta[318] 2.463625e-01 0.0005242409 0.02030376 2.088247e-01
## theta[319] 2.610323e-01 0.0007321813 0.02835726 2.079196e-01
## theta[320] 1.285939e-01 0.0011674430 0.04521487 5.379906e-02
## theta[321] 1.417688e-01 0.0012489024 0.04836978 6.093830e-02
## theta[322] 1.307790e-01 0.0011317121 0.04383102 5.714838e-02
## theta[323] 2.425819e-01 0.0007171890 0.02777661 1.908732e-01
## theta[324] 1.239073e-01 0.0011535777 0.04467787 5.260059e-02
## theta[325] 1.257067e-01 0.0011555232 0.04475322 5.053524e-02
## theta[326] 2.349755e-01 0.0011658752 0.04515415 1.513602e-01
## theta[327] 1.237543e-01 0.0011739943 0.04546860 5.030553e-02
## theta[328] 2.379244e-01 0.0010048277 0.03891681 1.655679e-01
## theta[329] 2.584327e-01 0.0007384536 0.02860018 2.068512e-01
## theta[330] 1.440149e-01 0.0012424148 0.04811852 6.421723e-02
## theta[331] 2.575584e-01 0.0004498814 0.01742383 2.243381e-01
## theta[332] 2.339572e-01 0.0005925550 0.02294956 1.896701e-01
## theta[333] 2.278273e-01 0.0005437392 0.02105893 1.881294e-01
## theta[334] 2.700722e-01 0.0004716213 0.01826581 2.352806e-01
## theta[335] 1.247705e-01 0.0012396223 0.04801037 4.718946e-02
## theta[336] 1.300124e-01 0.0012075271 0.04676732 5.452363e-02
## theta[337] 2.287440e-01 0.0009671795 0.03745870 1.588193e-01
## theta[338] 1.277008e-01 0.0012327262 0.04774328 5.040066e-02
## theta[339] 2.190249e-01 0.0006349650 0.02459209 1.711214e-01
## theta[340] 2.066810e-01 0.0005269083 0.02040707 1.675599e-01
## theta[341] 2.680057e-01 0.0007260444 0.02811958 2.101399e-01
## theta[342] 2.705810e-01 0.0005225729 0.02023916 2.315360e-01
## theta[343] 2.841804e-01 0.0004897153 0.01896659 2.485207e-01
## theta[344] 2.437367e-01 0.0009140859 0.03540239 1.780339e-01
## theta[345] 1.101397e-01 0.0007346314 0.02845215 6.049251e-02
## theta[346] 2.363285e-01 0.0004476658 0.01733802 2.035849e-01
## theta[347] 2.152705e-01 0.0006710355 0.02598909 1.679515e-01
## theta[348] 1.276740e-01 0.0011921026 0.04616994 5.242638e-02
## theta[349] 2.780010e-01 0.0005501765 0.02130825 2.389781e-01
## theta[350] 2.464640e-01 0.0004875356 0.01888217 2.085641e-01
## theta[351] 1.387396e-01 0.0011067291 0.04286343 6.377624e-02
## theta[352] 2.332106e-01 0.0011775214 0.04560521 1.496726e-01
## theta[353] 2.264545e-01 0.0010856887 0.04204854 1.489949e-01
## theta[354] 2.571531e-01 0.0004393570 0.01701622 2.247228e-01
## theta[355] 2.652184e-01 0.0011658000 0.04515124 1.853479e-01
## theta[356] 2.399443e-01 0.0008531852 0.03304372 1.771005e-01
## theta[357] 1.570923e-01 0.0012528897 0.04852421 7.548894e-02
## theta[358] 2.693022e-01 0.0006689698 0.02590909 2.195362e-01
## theta[359] 1.280203e-01 0.0012102231 0.04687174 5.085643e-02
## theta[360] 2.170297e-01 0.0008595064 0.03328854 1.562418e-01
## theta[361] 2.558550e-01 0.0011727512 0.04542046 1.718054e-01
## theta[362] 2.010249e-01 0.0007310434 0.02831319 1.468641e-01
## theta[363] 1.232988e-01 0.0011656705 0.04514622 4.934300e-02
## theta[364] 1.209513e-01 0.0007319920 0.02834993 7.271546e-02
## theta[365] 2.819516e-01 0.0004626342 0.01791774 2.458281e-01
## theta[366] 2.342814e-01 0.0007342116 0.02843589 1.812206e-01
## theta[367] 2.535435e-01 0.0004209489 0.01630328 2.211446e-01
## theta[368] 2.862378e-01 0.0004759596 0.01843383 2.524684e-01
## theta[369] 1.036401e-01 0.0007650655 0.02963086 5.062143e-02
## theta[370] 2.552915e-01 0.0003896873 0.01509253 2.265091e-01
## theta[371] 2.199901e-01 0.0006391021 0.02475232 1.725241e-01
## theta[372] 2.787462e-01 0.0004329773 0.01676914 2.456430e-01
## theta[373] 2.908491e-01 0.0008696941 0.03368311 2.282638e-01
## theta[374] 2.409216e-01 0.0008942400 0.03463377 1.763600e-01
## theta[375] 1.339523e-01 0.0011743167 0.04548109 5.736868e-02
## theta[376] 2.469985e-01 0.0005862796 0.02270651 2.039712e-01
## theta[377] 1.012808e-01 0.0010480274 0.04058993 3.847235e-02
## theta[378] 2.669780e-01 0.0005574685 0.02159066 2.239813e-01
## theta[379] 1.816365e-01 0.0010399113 0.04027559 1.127048e-01
## theta[380] 1.195877e-01 0.0010479730 0.04058782 5.289269e-02
## theta[381] 1.236110e-01 0.0011418216 0.04422256 4.854895e-02
## theta[382] 2.219698e-01 0.0008553631 0.03312807 1.620678e-01
## theta[383] 1.149566e-01 0.0010705126 0.04146077 4.515588e-02
## theta[384] 1.258413e-01 0.0008094546 0.03135004 7.014080e-02
## theta[385] 2.458650e-01 0.0009947932 0.03852817 1.761952e-01
## theta[386] 2.502753e-01 0.0005087415 0.01970347 2.113715e-01
## theta[387] 1.354765e-01 0.0008782783 0.03401557 7.536219e-02
## theta[388] 1.265718e-01 0.0011590345 0.04488921 5.429606e-02
## theta[389] 1.358509e-01 0.0012217151 0.04731682 6.023946e-02
## theta[390] 2.641794e-01 0.0004844831 0.01876395 2.260088e-01
## theta[391] 1.259795e-01 0.0011839286 0.04585336 4.831997e-02
## theta[392] 1.302234e-01 0.0010671124 0.04132909 5.936093e-02
## theta[393] 1.275594e-01 0.0011545003 0.04471360 4.985386e-02
## theta[394] 2.582394e-01 0.0005663130 0.02193321 2.175355e-01
## theta[395] 1.135472e-01 0.0010949325 0.04240655 4.563737e-02
## theta[396] 2.248891e-01 0.0004826565 0.01869321 1.895921e-01
## theta[397] 1.911807e-01 0.0008350646 0.03234191 1.297309e-01
## theta[398] 1.937137e-01 0.0006034975 0.02337336 1.502082e-01
## theta[399] 1.192024e-01 0.0011645043 0.04510106 4.514189e-02
## theta[400] 2.584507e-01 0.0009361267 0.03625603 1.901933e-01
## theta[401] 2.513585e-01 0.0005756758 0.02229583 2.101855e-01
## theta[402] 2.244725e-01 0.0007617455 0.02950228 1.692476e-01
## theta[403] 2.407119e-01 0.0008077029 0.03128220 1.822889e-01
## theta[404] 1.193184e-01 0.0011208017 0.04340846 4.889154e-02
## theta[405] 2.676383e-01 0.0004396921 0.01702920 2.349191e-01
## theta[406] 2.557667e-01 0.0004336335 0.01679455 2.240072e-01
## theta[407] 2.528980e-01 0.0004615733 0.01787666 2.179695e-01
## theta[408] 1.878151e-01 0.0011042523 0.04276751 1.098923e-01
## theta[409] 2.631869e-01 0.0010924706 0.04231120 1.843626e-01
## theta[410] 2.402487e-01 0.0011438195 0.04429994 1.551546e-01
## theta[411] 1.540458e-01 0.0012585461 0.04874328 6.901700e-02
## theta[412] 2.526807e-01 0.0004156714 0.01609888 2.214115e-01
## theta[413] 2.465728e-01 0.0006795477 0.02631877 1.965541e-01
## theta[414] 2.898082e-01 0.0005780361 0.02238724 2.482505e-01
## theta[415] 2.553569e-01 0.0007370952 0.02854758 2.021570e-01
## theta[416] 1.371156e-01 0.0011773553 0.04559877 5.704041e-02
## theta[417] 2.437439e-01 0.0005346972 0.02070873 2.036432e-01
## theta[418] 2.466373e-01 0.0006305701 0.02442188 2.011332e-01
## theta[419] 2.222764e-01 0.0008805421 0.03410325 1.598162e-01
## theta[420] 2.321860e-01 0.0009849866 0.03814837 1.587043e-01
## theta[421] 1.055332e-01 0.0009188333 0.03558626 4.659905e-02
## theta[422] 2.390362e-01 0.0004470097 0.01731261 2.055053e-01
## theta[423] 1.198835e-01 0.0009362171 0.03625953 5.565545e-02
## theta[424] 3.101532e-01 0.0005533877 0.02143261 2.691480e-01
## theta[425] 1.211474e-01 0.0010111987 0.03916356 5.414842e-02
## theta[426] 2.240161e-01 0.0006506677 0.02520025 1.761771e-01
## theta[427] 1.143897e-01 0.0008465505 0.03278676 5.665960e-02
## theta[428] 1.266923e-01 0.0011080687 0.04291531 5.363247e-02
## theta[429] 2.257315e-01 0.0004505422 0.01744942 1.936374e-01
## theta[430] 1.229415e-01 0.0010911032 0.04225825 5.368838e-02
## theta[431] 1.418221e-01 0.0012461439 0.04826294 6.245287e-02
## theta[432] 1.277507e-01 0.0011915501 0.04614854 5.071764e-02
## theta[433] 1.137655e-01 0.0009413746 0.03645928 5.329727e-02
## theta[434] 1.206329e-01 0.0010639619 0.04120707 5.112255e-02
## theta[435] 1.255936e-01 0.0012207167 0.04727815 5.038956e-02
## theta[436] 2.581637e-01 0.0009893207 0.03831623 1.875743e-01
## theta[437] 1.429178e-01 0.0012543014 0.04857888 5.956784e-02
## theta[438] 2.359720e-01 0.0009922045 0.03842791 1.634011e-01
## theta[439] 1.190776e-01 0.0011626113 0.04502774 4.311376e-02
## theta[440] 2.190490e-01 0.0005211410 0.02018370 1.810496e-01
## theta[441] 2.475068e-01 0.0005452655 0.02111804 2.055364e-01
## theta[442] 2.568618e-01 0.0004601423 0.01782123 2.232044e-01
## theta[443] 1.302388e-01 0.0012457825 0.04824895 5.087509e-02
## theta[444] 2.602847e-01 0.0010480935 0.04059249 1.846493e-01
## theta[445] 2.409736e-01 0.0004362365 0.01689537 2.085188e-01
## theta[446] 1.819526e-01 0.0011811844 0.04574708 1.020520e-01
## theta[447] 2.536297e-01 0.0007067686 0.02737303 2.010212e-01
## theta[448] 2.280462e-01 0.0008151261 0.03156970 1.689066e-01
## theta[449] 2.497943e-01 0.0004048935 0.01568146 2.200419e-01
## theta[450] 2.651493e-01 0.0005725259 0.02217383 2.242881e-01
## theta[451] 1.009185e-01 0.0007698824 0.02981742 4.931216e-02
## theta[452] 2.443644e-01 0.0011085172 0.04293269 1.624333e-01
## theta[453] 2.234383e-01 0.0006081319 0.02355285 1.785415e-01
## theta[454] 3.079303e-01 0.0004615108 0.01787424 2.744244e-01
## theta[455] 1.113870e-01 0.0008972418 0.03475003 5.573760e-02
## theta[456] 1.273633e-01 0.0011844663 0.04587418 5.139268e-02
## theta[457] 1.455059e-01 0.0011812916 0.04575123 6.994417e-02
## theta[458] 1.310183e-01 0.0012055438 0.04669051 5.453332e-02
## theta[459] 3.181856e-01 0.0005574031 0.02158813 2.772486e-01
## theta[460] 1.123730e-01 0.0008632874 0.03343498 5.575418e-02
## theta[461] 1.272673e-01 0.0012494070 0.04838932 4.701327e-02
## theta[462] 2.387006e-01 0.0006525668 0.02527380 1.916200e-01
## theta[463] 2.027168e-01 0.0004972963 0.01926020 1.676231e-01
## theta[464] 1.234517e-01 0.0011583105 0.04486117 4.656863e-02
## theta[465] 2.253390e-01 0.0008097305 0.03136073 1.654324e-01
## theta[466] 2.663854e-01 0.0005806011 0.02248658 2.226274e-01
## theta[467] 1.266066e-01 0.0010672387 0.04133398 5.905716e-02
## theta[468] 1.082270e-01 0.0007277935 0.02818732 6.030879e-02
## theta[469] 2.314074e-01 0.0006199207 0.02400943 1.848081e-01
## theta[470] 2.416368e-01 0.0006750132 0.02614315 1.879534e-01
## theta[471] 2.966769e-01 0.0005213190 0.02019060 2.584643e-01
## theta[472] 1.210201e-01 0.0011807368 0.04572974 4.762114e-02
## theta[473] 2.575439e-01 0.0006175385 0.02391716 2.134339e-01
## theta[474] 3.019707e-01 0.0005935174 0.02298683 2.597806e-01
## theta[475] 1.178052e-01 0.0011203189 0.04338976 4.736885e-02
## theta[476] 1.747927e-01 0.0010405845 0.04030166 1.010580e-01
## theta[477] 2.587059e-01 0.0005634291 0.02182152 2.191698e-01
## theta[478] 2.382879e-01 0.0008378266 0.03244888 1.804435e-01
## theta[479] 1.423345e-01 0.0009861884 0.03819491 7.603914e-02
## theta[480] 3.003043e-01 0.0005038018 0.01951216 2.629393e-01
## theta[481] 2.216248e-01 0.0005283068 0.02046124 1.808271e-01
## theta[482] 1.647576e-01 0.0009082235 0.03517534 1.023366e-01
## theta[483] 2.425659e-01 0.0006272820 0.02429453 1.984827e-01
## theta[484] 2.317912e-01 0.0008628539 0.03341819 1.710163e-01
## theta[485] 1.535471e-01 0.0012456293 0.04824302 7.209142e-02
## theta[486] 2.837888e-01 0.0004663304 0.01806090 2.468253e-01
## theta[487] 2.485086e-01 0.0008373089 0.03242884 1.847725e-01
## theta[488] 1.901978e-01 0.0008324863 0.03224206 1.290101e-01
## theta[489] 2.276495e-01 0.0007511149 0.02909056 1.736410e-01
## theta[490] 2.487930e-01 0.0006207180 0.02404030 2.027256e-01
## theta[491] 1.341974e-01 0.0012303219 0.04765016 5.445992e-02
## theta[492] 2.282834e-01 0.0005703026 0.02208772 1.866600e-01
## theta[493] 1.232915e-01 0.0011120689 0.04307024 4.933355e-02
## theta[494] 2.470404e-01 0.0005303576 0.02054066 2.071449e-01
## theta[495] 1.058189e-01 0.0009662823 0.03742395 4.217028e-02
## theta[496] 1.155496e-01 0.0009856601 0.03817445 4.929105e-02
## theta[497] 2.455313e-01 0.0005709369 0.02211229 2.029716e-01
## theta[498] 2.814071e-01 0.0004729977 0.01831912 2.453878e-01
## theta[499] 2.385311e-01 0.0005995364 0.02321994 1.925164e-01
## theta[500] 1.133451e-01 0.0007586193 0.02938120 5.996083e-02
## theta[501] 1.190536e-01 0.0010426039 0.04037988 5.126625e-02
## theta[502] 2.442856e-01 0.0004232574 0.01639269 2.138033e-01
## theta[503] 1.208882e-01 0.0010545978 0.04084440 5.395628e-02
## theta[504] 2.670667e-01 0.0005962275 0.02309179 2.228411e-01
## theta[505] 1.275511e-01 0.0011800148 0.04570178 5.126227e-02
## theta[506] 2.346713e-01 0.0005486117 0.02124764 1.947283e-01
## theta[507] 1.535899e-01 0.0012464238 0.04827379 7.219806e-02
## theta[508] 1.855713e-01 0.0007629126 0.02954748 1.284305e-01
## theta[509] 2.586382e-01 0.0004562953 0.01767224 2.252808e-01
## theta[510] 2.434918e-01 0.0006977435 0.02702349 1.933828e-01
## theta[511] 1.279079e-01 0.0011133861 0.04312126 5.502654e-02
## theta[512] 2.945739e-01 0.0005011193 0.01940827 2.578168e-01
## theta[513] 2.456402e-01 0.0005292761 0.02049878 2.045831e-01
## theta[514] 2.172143e-01 0.0006559388 0.02540440 1.696140e-01
## theta[515] 1.251934e-01 0.0011482352 0.04447096 5.204036e-02
## theta[516] 2.372876e-01 0.0010270237 0.03977646 1.654534e-01
## theta[517] 2.036228e-01 0.0008395547 0.03251581 1.426633e-01
## theta[518] 1.130776e-01 0.0010363141 0.04013627 4.642384e-02
## theta[519] 1.274251e-01 0.0012333913 0.04776904 5.078292e-02
## theta[520] 1.283677e-01 0.0012065993 0.04673139 5.480024e-02
## theta[521] 2.357824e-01 0.0005389152 0.02087210 1.960275e-01
## theta[522] 2.648778e-01 0.0004775095 0.01849386 2.277912e-01
## theta[523] 2.995050e-01 0.0006051634 0.02343788 2.548863e-01
## theta[524] 2.309682e-01 0.0009424216 0.03649983 1.657348e-01
## theta[525] 2.239450e-01 0.0004582885 0.01774944 1.904443e-01
## theta[526] 2.618858e-01 0.0006448457 0.02497477 2.164005e-01
## theta[527] 2.758751e-01 0.0004679633 0.01812414 2.413578e-01
## theta[528] 1.200822e-01 0.0011717670 0.04538234 4.713527e-02
## theta[529] 2.288756e-01 0.0004599333 0.01781314 1.940965e-01
## theta[530] 2.343877e-01 0.0006390145 0.02474893 1.878202e-01
## theta[531] 2.685531e-01 0.0004881732 0.01890687 2.334967e-01
## theta[532] 1.259565e-01 0.0011963571 0.04633471 4.767564e-02
## theta[533] 1.172261e-01 0.0008254426 0.03196925 6.358073e-02
## theta[534] 3.107267e-01 0.0006885559 0.02666766 2.580373e-01
## theta[535] 2.361092e-01 0.0010380396 0.04020310 1.573027e-01
## theta[536] 1.186204e-01 0.0010891113 0.04218110 4.807414e-02
## theta[537] 2.394000e-01 0.0004762860 0.01844648 2.036150e-01
## theta[538] 1.196765e-01 0.0010448745 0.04046782 5.258972e-02
## theta[539] 2.538174e-01 0.0005338537 0.02067607 2.137694e-01
## theta[540] 2.440585e-01 0.0009829741 0.03807042 1.727652e-01
## theta[541] 2.241452e-01 0.0010945155 0.04239040 1.452159e-01
## theta[542] 2.263535e-01 0.0009312468 0.03606703 1.608540e-01
## theta[543] 2.192937e-01 0.0009163790 0.03549121 1.553606e-01
## theta[544] 1.263546e-01 0.0009102666 0.03525447 6.405119e-02
## theta[545] 2.565581e-01 0.0011597121 0.04491546 1.725756e-01
## theta[546] 2.357432e-01 0.0005135762 0.01989072 1.977587e-01
## theta[547] 2.550868e-01 0.0011815829 0.04576251 1.722421e-01
## theta[548] 1.234137e-01 0.0011930104 0.04620510 4.893809e-02
## theta[549] 1.342016e-01 0.0009009771 0.03489469 7.257941e-02
## theta[550] 1.097042e-01 0.0007504481 0.02906473 6.118019e-02
## theta[551] 1.271141e-01 0.0011956069 0.04630566 5.193865e-02
## theta[552] 1.161514e-01 0.0010693429 0.04141547 4.733415e-02
## theta[553] 2.587986e-01 0.0004495744 0.01741194 2.261372e-01
## theta[554] 1.154903e-01 0.0010916099 0.04227787 4.719000e-02
## theta[555] 2.551989e-01 0.0008331234 0.03226673 1.946680e-01
## theta[556] 9.846576e-02 0.0007584615 0.02937509 4.872238e-02
## theta[557] 2.375765e-01 0.0009959594 0.03857334 1.669814e-01
## theta[558] 2.480275e-01 0.0007760591 0.03005664 1.921005e-01
## theta[559] 2.295668e-01 0.0009240521 0.03578838 1.638216e-01
## theta[560] 2.208348e-01 0.0008262291 0.03199971 1.612808e-01
## theta[561] 1.241695e-01 0.0011467597 0.04441381 4.964292e-02
## theta[562] 1.228715e-01 0.0011873418 0.04598555 4.871465e-02
## theta[563] 2.675616e-01 0.0005653302 0.02189515 2.264740e-01
## theta[564] 2.357862e-01 0.0005441041 0.02107306 1.946926e-01
## theta[565] 2.680136e-01 0.0010315623 0.03995224 1.927090e-01
## theta[566] 2.617272e-01 0.0007910852 0.03063860 2.015452e-01
## theta[567] 2.641180e-01 0.0006439450 0.02493988 2.153646e-01
## theta[568] 2.289721e-01 0.0006508331 0.02520666 1.812644e-01
## theta[569] 2.443258e-01 0.0004953251 0.01918386 2.072612e-01
## theta[570] 1.408675e-01 0.0008926605 0.03457259 8.128873e-02
## theta[571] 1.409629e-01 0.0011957223 0.04631013 6.270891e-02
## theta[572] 2.860553e-01 0.0006163061 0.02386943 2.412196e-01
## theta[573] 2.044004e-01 0.0010255067 0.03971770 1.305658e-01
## theta[574] 2.485643e-01 0.0011358176 0.04399003 1.666545e-01
## theta[575] 1.260731e-01 0.0012299477 0.04763567 5.099084e-02
## theta[576] 1.277808e-01 0.0012106546 0.04688845 4.982894e-02
## theta[577] 2.290726e-01 0.0005854725 0.02267525 1.856311e-01
## theta[578] 2.319916e-01 0.0010647179 0.04123635 1.539505e-01
## theta[579] 1.274597e-01 0.0012123501 0.04695412 5.039250e-02
## theta[580] 1.380173e-01 0.0012739494 0.04933985 5.832672e-02
## theta[581] 2.311938e-01 0.0010110139 0.03915640 1.584469e-01
## theta[582] 2.359052e-01 0.0005114413 0.01980804 1.985350e-01
## theta[583] 2.563954e-01 0.0007244080 0.02805620 2.020939e-01
## theta[584] 1.494470e-01 0.0008780093 0.03400515 9.053131e-02
## theta[585] 2.556946e-01 0.0005553678 0.02150930 2.153922e-01
## theta[586] 1.303169e-01 0.0012112554 0.04691172 5.019720e-02
## theta[587] 2.577016e-01 0.0006613862 0.02561538 2.073663e-01
## theta[588] 1.264201e-01 0.0011318188 0.04383515 5.374121e-02
## theta[589] 2.350003e-01 0.0011714886 0.04537156 1.509813e-01
## theta[590] 1.165735e-01 0.0008499211 0.03291730 6.111220e-02
## theta[591] 2.979486e-01 0.0004114956 0.01593716 2.671707e-01
## theta[592] 8.304519e-02 0.0006558470 0.02540085 3.888146e-02
## theta[593] 2.235779e-01 0.0007830872 0.03032884 1.630402e-01
## theta[594] 2.557857e-01 0.0005060129 0.01959779 2.179778e-01
## theta[595] 2.554667e-01 0.0007013409 0.02716282 2.046560e-01
## theta[596] 2.266945e-01 0.0004541799 0.01759031 1.938447e-01
## theta[597] 1.500938e-01 0.0011782591 0.04563378 7.147711e-02
## theta[598] 2.513371e-01 0.0004505856 0.01745111 2.167729e-01
## theta[599] 2.650224e-01 0.0004257702 0.01649001 2.335968e-01
## theta[600] 2.314786e-01 0.0007239359 0.02803792 1.807192e-01
## theta[601] 2.597860e-01 0.0006310684 0.02444117 2.153174e-01
## theta[602] 2.940155e-01 0.0004244927 0.01644053 2.628380e-01
## theta[603] 2.389931e-01 0.0006733676 0.02607941 1.920680e-01
## theta[604] 2.508495e-01 0.0009197553 0.03562197 1.850093e-01
## theta[605] 1.608184e-01 0.0008442460 0.03269751 1.020923e-01
## theta[606] 2.533037e-01 0.0008433940 0.03266451 1.939132e-01
## theta[607] 1.230616e-01 0.0011902674 0.04609886 4.550773e-02
## theta[608] 1.561821e-01 0.0008617413 0.03337510 9.856714e-02
## theta[609] 2.821988e-01 0.0005899173 0.02284740 2.390148e-01
## theta[610] 2.390206e-01 0.0008672257 0.03358751 1.764476e-01
## theta[611] 2.368310e-01 0.0007762208 0.03006290 1.818416e-01
## theta[612] 2.717587e-01 0.0008261414 0.03199632 2.111827e-01
## theta[613] 2.184645e-01 0.0006193080 0.02398570 1.731688e-01
## theta[614] 1.064151e-01 0.0008988769 0.03481335 4.835173e-02
## theta[615] 2.434437e-01 0.0008263894 0.03200592 1.834364e-01
## theta[616] 1.207367e-01 0.0010995581 0.04258570 5.013446e-02
## theta[617] 1.816712e-01 0.0011851912 0.04590226 1.046723e-01
## theta[618] 2.891046e-01 0.0004152001 0.01608063 2.570906e-01
## theta[619] 2.943220e-01 0.0005207705 0.02016936 2.555610e-01
## theta[620] 2.473608e-01 0.0008873839 0.03436823 1.848437e-01
## theta[621] 2.355744e-01 0.0008321272 0.03222815 1.740127e-01
## theta[622] 1.195432e-01 0.0011175035 0.04328073 4.709944e-02
## theta[623] 2.027537e-01 0.0007605064 0.02945429 1.490618e-01
## theta[624] 2.471906e-01 0.0004328095 0.01676264 2.151903e-01
## theta[625] 2.442834e-01 0.0005140724 0.01990994 2.070198e-01
## theta[626] 2.647300e-01 0.0008443293 0.03270073 2.036359e-01
## theta[627] 1.247801e-01 0.0011914743 0.04614560 4.799522e-02
## theta[628] 3.282737e-01 0.0005062708 0.01960778 2.888911e-01
## theta[629] 2.613207e-01 0.0012212342 0.04729820 1.741097e-01
## theta[630] 1.249299e-01 0.0011923548 0.04617970 4.817062e-02
## theta[631] 2.718286e-01 0.0004311791 0.01669949 2.413765e-01
## theta[632] 1.244280e-01 0.0011668234 0.04519088 4.823806e-02
## theta[633] 2.831022e-01 0.0004557615 0.01765157 2.506263e-01
## theta[634] 2.602374e-01 0.0005075132 0.01965590 2.233967e-01
## theta[635] 2.080772e-01 0.0007137118 0.02764194 1.536525e-01
## theta[636] 2.346628e-01 0.0006215335 0.02407189 1.903789e-01
## theta[637] 2.482848e-01 0.0004722363 0.01828963 2.134169e-01
## theta[638] 2.725819e-01 0.0004316031 0.01671591 2.407058e-01
## theta[639] 1.157126e-01 0.0011288148 0.04371881 4.260048e-02
## theta[640] 3.201225e-01 0.0004609614 0.01785296 2.868909e-01
## theta[641] 2.151839e-01 0.0006738118 0.02609662 1.661224e-01
## theta[642] 2.778230e-01 0.0004691160 0.01816878 2.431678e-01
## theta[643] 2.263325e-01 0.0005327033 0.02063151 1.869826e-01
## theta[644] 2.503453e-01 0.0004511305 0.01747221 2.172024e-01
## theta[645] 2.598437e-01 0.0007169246 0.02776637 2.077248e-01
## theta[646] 2.275622e-01 0.0006615316 0.02562101 1.796936e-01
## theta[647] 2.208253e-01 0.0009833060 0.03808328 1.483354e-01
## theta[648] 1.297679e-01 0.0012616257 0.04886255 5.137013e-02
## theta[649] 1.145769e-01 0.0008919664 0.03454571 5.602845e-02
## theta[650] 2.676895e-01 0.0008315370 0.03220529 2.064787e-01
## theta[651] 2.176100e-01 0.0010379056 0.04019791 1.451839e-01
## theta[652] 1.240790e-01 0.0012239012 0.04740149 4.815115e-02
## theta[653] 2.239629e-01 0.0008749479 0.03388659 1.595007e-01
## theta[654] 1.003769e-01 0.0007509259 0.02908323 5.004382e-02
## theta[655] 2.830575e-01 0.0005043192 0.01953220 2.464503e-01
## theta[656] 2.439503e-01 0.0004263833 0.01651375 2.126450e-01
## theta[657] 2.298244e-01 0.0005173470 0.02003676 1.911566e-01
## theta[658] 2.036865e-01 0.0007101140 0.02750260 1.531545e-01
## theta[659] 2.267430e-01 0.0009618162 0.03725098 1.584577e-01
## theta[660] 1.336304e-01 0.0011195132 0.04335856 5.898169e-02
## theta[661] 3.165938e-01 0.0004849795 0.01878318 2.793689e-01
## theta[662] 1.224722e-01 0.0011937514 0.04623379 4.768134e-02
## theta[663] 2.232912e-01 0.0008746935 0.03387673 1.591496e-01
## theta[664] 2.700038e-01 0.0005506373 0.02132609 2.297864e-01
## theta[665] 2.389149e-01 0.0007310383 0.02831299 1.846594e-01
## theta[666] 2.163697e-01 0.0007584606 0.02937505 1.626924e-01
## theta[667] 2.425667e-01 0.0005803031 0.02247504 2.010742e-01
## theta[668] 2.580215e-01 0.0006201917 0.02401992 2.118193e-01
## theta[669] 2.361092e-01 0.0010762216 0.04168188 1.563361e-01
## theta[670] 1.281519e-01 0.0011677248 0.04522579 5.438095e-02
## theta[671] 1.168301e-01 0.0009113496 0.03529642 5.570836e-02
## theta[672] 1.258912e-01 0.0011067074 0.04286259 5.480149e-02
## theta[673] 2.741795e-01 0.0004922895 0.01906629 2.380616e-01
## theta[674] 1.264195e-01 0.0011608846 0.04496087 5.316789e-02
## theta[675] 2.370020e-01 0.0009959176 0.03857172 1.605821e-01
## theta[676] 1.815598e-01 0.0005977050 0.02314901 1.381100e-01
## theta[677] 2.323700e-01 0.0007939148 0.03074819 1.740872e-01
## theta[678] 2.902131e-01 0.0004972588 0.01925875 2.512529e-01
## theta[679] 2.320536e-01 0.0006814385 0.02639200 1.814250e-01
## theta[680] 2.687295e-01 0.0004671362 0.01809211 2.341344e-01
## theta[681] 1.253256e-01 0.0011712766 0.04536335 4.743135e-02
## theta[682] 2.732963e-01 0.0008839810 0.03423644 2.078168e-01
## theta[683] 2.422012e-01 0.0005385564 0.02085820 2.005837e-01
## theta[684] 2.708168e-01 0.0004646488 0.01799577 2.352162e-01
## theta[685] 2.465156e-01 0.0006990274 0.02707322 1.968399e-01
## theta[686] 2.400085e-01 0.0007332571 0.02839893 1.876741e-01
## theta[687] 2.298473e-01 0.0010988782 0.04255937 1.494571e-01
## theta[688] 2.169503e-01 0.0005534820 0.02143627 1.759392e-01
## theta[689] 2.800181e-01 0.0005645114 0.02186343 2.388478e-01
## theta[690] 1.216915e-01 0.0008656680 0.03352718 6.177658e-02
## theta[691] 2.804315e-01 0.0004718012 0.01827278 2.445977e-01
## theta[692] 2.061175e-01 0.0006639823 0.02571592 1.579027e-01
## theta[693] 2.902190e-01 0.0004583842 0.01775314 2.560093e-01
## theta[694] 9.495220e-02 0.0006992712 0.02708266 4.846637e-02
## theta[695] 2.471141e-01 0.0004414306 0.01709653 2.147266e-01
## theta[696] 2.817591e-01 0.0005899771 0.02284972 2.396414e-01
## theta[697] 2.291698e-01 0.0007012726 0.02716017 1.769398e-01
## theta[698] 2.869994e-01 0.0009212950 0.03568160 2.200734e-01
## theta[699] 2.708328e-01 0.0009383826 0.03634340 2.029637e-01
## theta[700] 2.319724e-01 0.0006730918 0.02606873 1.820094e-01
## theta[701] 1.265791e-01 0.0012222779 0.04733862 5.106683e-02
## theta[702] 1.358046e-01 0.0011824748 0.04579705 5.843662e-02
## theta[703] 2.570659e-01 0.0005529776 0.02141673 2.165321e-01
## theta[704] 3.055969e-01 0.0004779084 0.01850931 2.707368e-01
## theta[705] 2.547113e-01 0.0005756569 0.02229509 2.131051e-01
## theta[706] 2.617247e-01 0.0004808838 0.01862455 2.257603e-01
## theta[707] 2.633495e-01 0.0012129069 0.04697568 1.771356e-01
## theta[708] 2.555375e-01 0.0004944689 0.01915070 2.178669e-01
## theta[709] 2.480814e-01 0.0012001362 0.04648108 1.597949e-01
## theta[710] 2.199139e-01 0.0005948399 0.02303805 1.774589e-01
## theta[711] 1.650487e-01 0.0010534248 0.04079897 9.474408e-02
## theta[712] 1.383516e-01 0.0011890254 0.04605076 6.173293e-02
## theta[713] 1.387353e-01 0.0009326313 0.03612065 7.736983e-02
## theta[714] 2.423188e-01 0.0004999356 0.01936242 2.060566e-01
## theta[715] 2.470725e-01 0.0010055551 0.03894498 1.751369e-01
## theta[716] 2.774245e-01 0.0006001132 0.02324228 2.334409e-01
## theta[717] 2.179886e-01 0.0010499494 0.04066437 1.414443e-01
## theta[718] 1.246769e-01 0.0011026750 0.04270642 5.498089e-02
## theta[719] 1.276348e-01 0.0012127560 0.04696984 5.066152e-02
## theta[720] 2.393048e-01 0.0006889697 0.02668368 1.870856e-01
## theta[721] 1.229611e-01 0.0012048933 0.04666532 4.582984e-02
## theta[722] 2.327355e-01 0.0003900413 0.01510623 2.030642e-01
## theta[723] 1.464430e-01 0.0008639322 0.03345995 8.849800e-02
## theta[724] 1.369843e-01 0.0011931554 0.04621071 5.680873e-02
## theta[725] 2.639293e-01 0.0008414636 0.03258974 2.018857e-01
## theta[726] 2.434685e-01 0.0009352071 0.03622041 1.785566e-01
## theta[727] 1.278314e-01 0.0011752575 0.04551753 5.284517e-02
## theta[728] 1.250848e-01 0.0012012472 0.04652410 4.928663e-02
## theta[729] 2.186854e-01 0.0004850453 0.01878572 1.819682e-01
## theta[730] 3.042516e-01 0.0004381352 0.01696890 2.721229e-01
## theta[731] 2.134992e-01 0.0005159363 0.01998213 1.764210e-01
## theta[732] 2.779290e-01 0.0006184204 0.02395132 2.324867e-01
## theta[733] 1.292609e-01 0.0011978274 0.04639165 5.368952e-02
## theta[734] 2.554430e-01 0.0007325815 0.02837276 2.026488e-01
## theta[735] 2.478283e-01 0.0009147102 0.03542657 1.841819e-01
## theta[736] 8.967091e-02 0.0007508083 0.02907868 4.120624e-02
## theta[737] 1.150086e-01 0.0010070964 0.03900467 5.202808e-02
## theta[738] 1.489507e-01 0.0008960296 0.03470308 8.605483e-02
## theta[739] 2.826359e-01 0.0004848634 0.01877868 2.470211e-01
## theta[740] 2.594596e-01 0.0008259352 0.03198833 1.999490e-01
## theta[741] 2.155539e-01 0.0004398376 0.01703484 1.815550e-01
## theta[742] 1.151961e-01 0.0008965459 0.03472307 5.631865e-02
## theta[743] 2.691111e-01 0.0004621568 0.01789926 2.348403e-01
## theta[744] 2.303704e-01 0.0006985053 0.02705300 1.825202e-01
## theta[745] 2.666822e-01 0.0005679807 0.02199780 2.230196e-01
## theta[746] 2.294992e-01 0.0005669390 0.02195745 1.900330e-01
## theta[747] 2.451887e-01 0.0007726164 0.02992331 1.907324e-01
## theta[748] 2.479368e-01 0.0011307038 0.04379197 1.675682e-01
## theta[749] 1.878444e-01 0.0006550249 0.02536901 1.410441e-01
## theta[750] 2.696965e-01 0.0005109150 0.01978765 2.309135e-01
## theta[751] 1.269179e-01 0.0012382685 0.04795793 5.030467e-02
## theta[752] 1.962202e-01 0.0005954903 0.02306324 1.511155e-01
## theta[753] 2.374225e-01 0.0004724949 0.01829965 2.017882e-01
## theta[754] 2.599169e-01 0.0006486921 0.02512374 2.129562e-01
## theta[755] 2.645938e-01 0.0005222958 0.02022843 2.265339e-01
## theta[756] 1.102072e-01 0.0007604665 0.02945274 5.738330e-02
## theta[757] 1.287196e-01 0.0011586371 0.04487382 5.648018e-02
## theta[758] 2.479936e-01 0.0007706769 0.02984819 1.895589e-01
## theta[759] 2.788643e-01 0.0004381500 0.01696948 2.471838e-01
## theta[760] 2.878391e-01 0.0006284530 0.02433988 2.427137e-01
## theta[761] 2.555666e-01 0.0007932828 0.03072371 1.980457e-01
## theta[762] 1.269403e-01 0.0011971428 0.04636514 5.117679e-02
## theta[763] 2.474732e-01 0.0010374845 0.04018160 1.702879e-01
## theta[764] 1.426787e-01 0.0012704662 0.04920494 6.018662e-02
## theta[765] 2.111776e-01 0.0007964965 0.03084818 1.484791e-01
## theta[766] 1.292035e-01 0.0010960300 0.04244906 6.154625e-02
## theta[767] 1.361335e-01 0.0012168348 0.04712781 5.791764e-02
## theta[768] 2.596606e-01 0.0005012358 0.01941278 2.237219e-01
## theta[769] 1.262838e-01 0.0012183619 0.04718695 5.082451e-02
## theta[770] 2.559490e-01 0.0006419038 0.02486083 2.094583e-01
## theta[771] 2.816499e-01 0.0006582521 0.02549399 2.362344e-01
## theta[772] 2.480859e-01 0.0005376335 0.02082246 2.072653e-01
## theta[773] 2.267763e-01 0.0008855433 0.03429694 1.618974e-01
## theta[774] 2.314470e-01 0.0010215444 0.03956424 1.554224e-01
## theta[775] 2.227451e-01 0.0005232908 0.02026697 1.836087e-01
## theta[776] 2.422080e-01 0.0004921123 0.01905943 2.054635e-01
## theta[777] 1.279967e-01 0.0011839683 0.04585490 5.074392e-02
## theta[778] 2.537317e-01 0.0006460162 0.02502010 2.077305e-01
## theta[779] 2.553690e-01 0.0004292111 0.01662327 2.245595e-01
## theta[780] 1.187022e-01 0.0008941214 0.03462917 5.917112e-02
## theta[781] 1.603027e-01 0.0013102477 0.05074568 7.887240e-02
## theta[782] 2.168709e-01 0.0005948834 0.02303973 1.715669e-01
## theta[783] 2.683147e-01 0.0006026786 0.02334164 2.245634e-01
## theta[784] 2.796021e-01 0.0004354093 0.01686333 2.478866e-01
## theta[785] 2.532590e-01 0.0007014606 0.02716745 2.043955e-01
## theta[786] 2.298116e-01 0.0005742176 0.02223935 1.883908e-01
## theta[787] 1.497533e-01 0.0011870092 0.04597267 7.572540e-02
## theta[788] 2.012198e-01 0.0010479325 0.04058625 1.303223e-01
## theta[789] 1.874790e-01 0.0010412352 0.04032687 1.141422e-01
## theta[790] 1.271977e-01 0.0012149383 0.04705436 4.885570e-02
## theta[791] 2.124885e-01 0.0006357939 0.02462419 1.668796e-01
## theta[792] 1.263750e-01 0.0011466095 0.04440800 5.228536e-02
## theta[793] 2.431866e-01 0.0007101054 0.02750227 1.901227e-01
## theta[794] 2.460608e-01 0.0010637584 0.04119919 1.705085e-01
## theta[795] 2.346303e-01 0.0011262343 0.04361887 1.527220e-01
## theta[796] 2.222373e-01 0.0008768503 0.03396027 1.591250e-01
## theta[797] 2.165085e-01 0.0007499836 0.02904674 1.612956e-01
## theta[798] 2.065925e-01 0.0008474347 0.03282100 1.453311e-01
## theta[799] 1.143998e-01 0.0009867617 0.03821712 4.997174e-02
## theta[800] 2.427198e-01 0.0010726713 0.04154438 1.617393e-01
## theta[801] 2.427573e-01 0.0009852737 0.03815949 1.703581e-01
## theta[802] 1.249157e-01 0.0012017175 0.04654232 4.581323e-02
## theta[803] 2.433896e-01 0.0011284870 0.04370611 1.630830e-01
## theta[804] 1.732789e-01 0.0009568652 0.03705923 1.061294e-01
## theta[805] 1.088207e-01 0.0007951556 0.03079624 5.401213e-02
## theta[806] 1.271937e-01 0.0011574299 0.04482707 5.305285e-02
## theta[807] 2.690424e-01 0.0005162528 0.01999438 2.311764e-01
## theta[808] 2.420519e-01 0.0005835392 0.02260038 1.995251e-01
## theta[809] 1.301433e-01 0.0012246479 0.04743041 5.097045e-02
## theta[810] 1.509829e-01 0.0011982560 0.04640825 7.683522e-02
## theta[811] 1.283046e-01 0.0011955880 0.04630492 5.179380e-02
## theta[812] 7.626179e-02 0.0006956767 0.02694344 3.265782e-02
## theta[813] 1.291603e-01 0.0012007908 0.04650643 5.510693e-02
## theta[814] 1.381903e-01 0.0011725347 0.04541207 6.139485e-02
## theta[815] 2.528684e-01 0.0009004735 0.03487519 1.874987e-01
## theta[816] 2.612749e-01 0.0007098192 0.02749118 2.112493e-01
## theta[817] 1.254280e-01 0.0011818241 0.04577185 5.138404e-02
## theta[818] 2.475783e-01 0.0007425715 0.02875967 1.952868e-01
## theta[819] 1.267727e-01 0.0012231127 0.04737095 4.780004e-02
## theta[820] 3.035744e-01 0.0004583730 0.01775271 2.681747e-01
## theta[821] 1.236599e-01 0.0011108554 0.04302325 5.073536e-02
## theta[822] 2.367681e-01 0.0007793999 0.03018603 1.783702e-01
## theta[823] 2.552904e-01 0.0007039494 0.02726384 2.062447e-01
## theta[824] 2.555647e-01 0.0006882618 0.02665626 2.042709e-01
## theta[825] 1.583599e-01 0.0009505707 0.03681544 9.516030e-02
## theta[826] 2.331989e-01 0.0007002501 0.02712057 1.806718e-01
## theta[827] 1.197977e-01 0.0011457399 0.04437431 4.777778e-02
## theta[828] 1.259013e-01 0.0007790450 0.03017228 7.320597e-02
## theta[829] 2.386205e-01 0.0004820638 0.01867025 2.023101e-01
## theta[830] 2.746413e-01 0.0006961069 0.02696010 2.263603e-01
## theta[831] 2.193175e-01 0.0009961361 0.03858018 1.473671e-01
## theta[832] 2.394525e-01 0.0005365863 0.02078190 1.994041e-01
## theta[833] 1.563522e-01 0.0011527302 0.04464505 7.783612e-02
## theta[834] 1.220946e-01 0.0010855103 0.04204163 5.162524e-02
## theta[835] 2.833162e-01 0.0005075929 0.01965899 2.449996e-01
## theta[836] 2.247339e-01 0.0007303725 0.02828721 1.723827e-01
## theta[837] 2.490818e-01 0.0012050331 0.04667073 1.662057e-01
## theta[838] 2.347719e-01 0.0005238126 0.02028717 1.944721e-01
## theta[839] 2.581067e-01 0.0006728901 0.02606092 2.083837e-01
## theta[840] 2.432256e-01 0.0006905084 0.02674328 1.933831e-01
## theta[841] 1.113806e-01 0.0010923516 0.04230660 4.211122e-02
## theta[842] 1.339077e-01 0.0011914176 0.04614341 5.971924e-02
## theta[843] 1.250872e-01 0.0011676038 0.04522110 5.356413e-02
## theta[844] 1.175165e-01 0.0011661101 0.04516325 4.444001e-02
## theta[845] 1.130863e-01 0.0009124446 0.03533883 5.283473e-02
## theta[846] 2.367864e-01 0.0005846695 0.02264415 1.919777e-01
## theta[847] 1.289403e-01 0.0011801192 0.04570582 5.380823e-02
## theta[848] 1.579678e-01 0.0012260795 0.04748585 8.108941e-02
## theta[849] 2.114000e-01 0.0008073977 0.03127038 1.534213e-01
## theta[850] 1.435520e-01 0.0012184673 0.04719104 6.299593e-02
## theta[851] 1.206425e-01 0.0010662279 0.04129483 5.123631e-02
## theta[852] 1.527561e-01 0.0008672501 0.03358845 9.504312e-02
## theta[853] 9.402462e-02 0.0006737740 0.02609515 4.866327e-02
## theta[854] 2.560106e-01 0.0007025756 0.02721063 2.047818e-01
## theta[855] 1.230700e-01 0.0011655356 0.04514100 5.059472e-02
## theta[856] 2.674610e-01 0.0008379197 0.03245249 2.106688e-01
## theta[857] 2.643904e-01 0.0005704706 0.02209423 2.244592e-01
## theta[858] 2.799853e-01 0.0006332199 0.02452450 2.342476e-01
## theta[859] 2.374856e-01 0.0007332391 0.02839823 1.838512e-01
## theta[860] 2.621442e-01 0.0005097761 0.01974355 2.252247e-01
## theta[861] 2.914720e-01 0.0005770905 0.02235062 2.485997e-01
## theta[862] 2.094525e-01 0.0009100398 0.03524569 1.423546e-01
## theta[863] 2.601293e-01 0.0005229723 0.02025463 2.223479e-01
## theta[864] 2.548520e-01 0.0008788933 0.03403939 1.900955e-01
## theta[865] 2.184134e-01 0.0006282632 0.02433253 1.737406e-01
## theta[866] 1.268479e-01 0.0010930086 0.04233204 5.539680e-02
## theta[867] 2.352755e-01 0.0007761963 0.03006195 1.784470e-01
## theta[868] 1.283102e-01 0.0011890597 0.04605208 5.206857e-02
## theta[869] 2.102801e-01 0.0006643443 0.02572994 1.603431e-01
## theta[870] 2.794728e-01 0.0008399848 0.03253247 2.184927e-01
## theta[871] 3.035225e-01 0.0004702111 0.01821120 2.695690e-01
## theta[872] 2.209673e-01 0.0008859983 0.03431457 1.542025e-01
## theta[873] 2.287691e-01 0.0007983691 0.03092070 1.690135e-01
## theta[874] 2.786677e-01 0.0007329904 0.02838859 2.263557e-01
## theta[875] 2.839548e-01 0.0004812727 0.01863961 2.478644e-01
## theta[876] 2.701581e-01 0.0004627365 0.01792171 2.356856e-01
## theta[877] 2.300468e-01 0.0006420845 0.02486783 1.846238e-01
## theta[878] 1.492317e-01 0.0008603311 0.03332048 9.112885e-02
## theta[879] 1.403136e-01 0.0012093490 0.04683788 6.113623e-02
## theta[880] 2.521725e-01 0.0004514467 0.01748446 2.184267e-01
## theta[881] 2.357268e-01 0.0006427487 0.02489355 1.892092e-01
## theta[882] 1.323842e-01 0.0012798576 0.04956867 5.004542e-02
## theta[883] 1.275686e-01 0.0011497782 0.04453072 5.120260e-02
## theta[884] 2.375149e-01 0.0010587415 0.04100488 1.605703e-01
## theta[885] 2.459419e-01 0.0004216026 0.01632860 2.148393e-01
## theta[886] 1.605298e-01 0.0010694985 0.04142150 9.091877e-02
## gamma[1] -1.091988e+00 0.0009231036 0.03575165 -1.164547e+00
## gamma[2] -1.094206e+00 0.0010157254 0.03933888 -1.172159e+00
## gamma[3] -1.068985e+00 0.0009222947 0.03572032 -1.144651e+00
## gamma[4] -1.168003e+00 0.0009066370 0.03511390 -1.236130e+00
## gamma[5] -1.049651e+00 0.0010274644 0.03979353 -1.125180e+00
## gamma[6] -1.105816e+00 0.0008102677 0.03138153 -1.168925e+00
## gamma[7] -1.904471e+00 0.0022542654 0.05592965 -2.014731e+00
## gamma[8] -1.054569e+00 0.0009770183 0.03783976 -1.126325e+00
## gamma[9] -1.102448e+00 0.0011340508 0.04392160 -1.190221e+00
## alpha_w 1.953644e-02 0.0004611858 0.01786165 -1.590565e-02
## alpha_h -8.574784e-03 0.0004555703 0.01764416 -4.404191e-02
## kappa[1] 1.076298e+02 0.7297831360 23.02487981 6.763837e+01
## kappa[2] 1.043302e+02 0.6067630003 23.49982995 6.539512e+01
## kappa[3] 9.616091e+01 0.5391578008 20.88149183 6.059793e+01
## kappa[4] 9.026832e+01 0.5881898154 18.87312557 5.809734e+01
## kappa[5] 9.497217e+01 0.5953832245 23.05909313 5.710838e+01
## kappa[6] 1.067727e+02 0.7887826886 22.34440844 6.894109e+01
## kappa[7] 5.349889e+01 1.1560027652 13.08324099 3.162945e+01
## kappa[8] 1.104142e+02 0.7060202038 27.34404491 6.468716e+01
## kappa[9] 9.028415e+01 0.5593586335 21.66386672 5.369858e+01
## lp__ -8.740359e+04 3.4004625556 39.87532761 -8.748668e+04
## 25% 50% 75% 97.5%
## theta[1] 1.951215e-01 2.143713e-01 2.349924e-01 2.734493e-01
## theta[2] 8.045232e-02 9.912715e-02 1.199150e-01 1.605264e-01
## theta[3] 2.832958e-01 2.948404e-01 3.074972e-01 3.310207e-01
## theta[4] 9.324965e-02 1.197271e-01 1.543228e-01 2.266748e-01
## theta[5] 9.535680e-02 1.217466e-01 1.550701e-01 2.296643e-01
## theta[6] 2.023971e-01 2.133230e-01 2.248273e-01 2.483444e-01
## theta[7] 2.726866e-01 2.836754e-01 2.948042e-01 3.158651e-01
## theta[8] 2.407548e-01 2.584251e-01 2.774427e-01 3.158879e-01
## theta[9] 2.564613e-01 2.684270e-01 2.802335e-01 3.035586e-01
## theta[10] 2.403598e-01 2.528710e-01 2.674102e-01 2.943448e-01
## theta[11] 2.013284e-01 2.303461e-01 2.576947e-01 3.183319e-01
## theta[12] 9.719501e-02 1.221326e-01 1.522639e-01 2.138843e-01
## theta[13] 2.149515e-01 2.349536e-01 2.559548e-01 2.968035e-01
## theta[14] 1.024934e-01 1.240313e-01 1.450681e-01 1.899446e-01
## theta[15] 2.346086e-01 2.532370e-01 2.713622e-01 3.115017e-01
## theta[16] 3.015945e-01 3.127064e-01 3.241363e-01 3.492871e-01
## theta[17] 2.018229e-01 2.240762e-01 2.468849e-01 2.926976e-01
## theta[18] 2.816705e-01 2.921957e-01 3.027083e-01 3.237812e-01
## theta[19] 2.213723e-01 2.442099e-01 2.694817e-01 3.136373e-01
## theta[20] 2.695939e-01 2.795345e-01 2.918664e-01 3.121097e-01
## theta[21] 2.419084e-01 2.538970e-01 2.655927e-01 2.911424e-01
## theta[22] 2.193755e-01 2.448082e-01 2.722098e-01 3.244698e-01
## theta[23] 2.750719e-01 2.858590e-01 2.974128e-01 3.197729e-01
## theta[24] 2.649983e-01 2.766145e-01 2.895764e-01 3.129888e-01
## theta[25] 2.288628e-01 2.416144e-01 2.545899e-01 2.793124e-01
## theta[26] 2.089645e-01 2.321906e-01 2.593083e-01 3.110308e-01
## theta[27] 2.778479e-01 2.888945e-01 2.994612e-01 3.187923e-01
## theta[28] 9.221608e-02 1.187986e-01 1.488029e-01 2.160088e-01
## theta[29] 2.193170e-01 2.382861e-01 2.575589e-01 2.943490e-01
## theta[30] 2.250975e-01 2.387174e-01 2.531805e-01 2.796355e-01
## theta[31] 2.850669e-01 2.958411e-01 3.084804e-01 3.302757e-01
## theta[32] 2.563768e-01 2.688522e-01 2.826234e-01 3.068123e-01
## theta[33] 1.215410e-01 1.453062e-01 1.706059e-01 2.248092e-01
## theta[34] 2.516223e-01 2.618374e-01 2.723044e-01 2.941556e-01
## theta[35] 2.258376e-01 2.406736e-01 2.550970e-01 2.841462e-01
## theta[36] 2.275741e-01 2.420390e-01 2.563272e-01 2.891282e-01
## theta[37] 1.068884e-01 1.391340e-01 1.741119e-01 2.486488e-01
## theta[38] 2.482816e-01 2.598483e-01 2.715299e-01 2.933594e-01
## theta[39] 9.275794e-02 1.190983e-01 1.488017e-01 2.175049e-01
## theta[40] 1.950537e-01 2.231290e-01 2.528334e-01 3.197315e-01
## theta[41] 2.822766e-01 2.964921e-01 3.111732e-01 3.353287e-01
## theta[42] 2.670736e-01 2.796428e-01 2.917560e-01 3.153738e-01
## theta[43] 2.547136e-01 2.730674e-01 2.932080e-01 3.313137e-01
## theta[44] 2.230561e-01 2.359291e-01 2.490382e-01 2.748031e-01
## theta[45] 1.000250e-01 1.274575e-01 1.559172e-01 2.303280e-01
## theta[46] 3.062308e-01 3.182421e-01 3.294619e-01 3.507541e-01
## theta[47] 2.432921e-01 2.747834e-01 3.090296e-01 3.715723e-01
## theta[48] 9.193003e-02 1.189197e-01 1.459329e-01 2.194435e-01
## theta[49] 1.981197e-01 2.137400e-01 2.292632e-01 2.584689e-01
## theta[50] 2.875708e-01 3.028050e-01 3.174241e-01 3.482965e-01
## theta[51] 2.039931e-01 2.219100e-01 2.428670e-01 2.823702e-01
## theta[52] 1.043989e-01 1.343949e-01 1.681865e-01 2.435594e-01
## theta[53] 1.139519e-01 1.470913e-01 1.836378e-01 2.605534e-01
## theta[54] 2.713895e-01 2.835633e-01 2.948365e-01 3.182717e-01
## theta[55] 9.270395e-02 1.154061e-01 1.411641e-01 1.967677e-01
## theta[56] 1.023214e-01 1.258423e-01 1.513437e-01 2.063257e-01
## theta[57] 2.180659e-01 2.348847e-01 2.526674e-01 2.853603e-01
## theta[58] 1.845726e-01 2.068198e-01 2.282320e-01 2.792850e-01
## theta[59] 2.627215e-01 2.774608e-01 2.925482e-01 3.207708e-01
## theta[60] 8.884701e-02 1.177223e-01 1.533912e-01 2.241316e-01
## theta[61] 2.816276e-01 2.931413e-01 3.052017e-01 3.284592e-01
## theta[62] 8.218190e-02 1.088444e-01 1.375406e-01 2.056684e-01
## theta[63] 2.557216e-01 2.670975e-01 2.789331e-01 3.041570e-01
## theta[64] 2.058297e-01 2.256509e-01 2.479457e-01 2.937968e-01
## theta[65] 2.817608e-01 2.940552e-01 3.059789e-01 3.321048e-01
## theta[66] 2.290318e-01 2.472317e-01 2.674749e-01 3.040972e-01
## theta[67] 2.529721e-01 2.777780e-01 3.043446e-01 3.509485e-01
## theta[68] 9.511057e-02 1.226430e-01 1.565467e-01 2.246606e-01
## theta[69] 8.197364e-02 9.873907e-02 1.189455e-01 1.634431e-01
## theta[70] 9.715633e-02 1.251759e-01 1.571895e-01 2.263778e-01
## theta[71] 2.262029e-01 2.433386e-01 2.626385e-01 2.927530e-01
## theta[72] 2.741363e-01 2.866484e-01 2.991072e-01 3.215691e-01
## theta[73] 7.450337e-02 9.787596e-02 1.253958e-01 1.840615e-01
## theta[74] 2.563935e-01 2.677532e-01 2.798875e-01 3.024497e-01
## theta[75] 2.928541e-01 3.047508e-01 3.167494e-01 3.422001e-01
## theta[76] 9.574323e-02 1.218431e-01 1.541623e-01 2.214403e-01
## theta[77] 2.017332e-01 2.241896e-01 2.465460e-01 3.026187e-01
## theta[78] 1.934658e-01 2.204582e-01 2.513154e-01 3.094440e-01
## theta[79] 2.046429e-01 2.295269e-01 2.564228e-01 3.110214e-01
## theta[80] 2.296787e-01 2.454729e-01 2.612087e-01 2.960842e-01
## theta[81] 2.032324e-01 2.207454e-01 2.395978e-01 2.744669e-01
## theta[82] 9.419338e-02 1.239723e-01 1.567414e-01 2.299216e-01
## theta[83] 9.454725e-02 1.226033e-01 1.543659e-01 2.347431e-01
## theta[84] 9.401251e-02 1.225920e-01 1.561932e-01 2.376020e-01
## theta[85] 1.116313e-01 1.404068e-01 1.720151e-01 2.382539e-01
## theta[86] 9.740578e-02 1.271137e-01 1.614709e-01 2.389193e-01
## theta[87] 1.054869e-01 1.368691e-01 1.695891e-01 2.465155e-01
## theta[88] 2.030614e-01 2.286866e-01 2.539683e-01 3.057655e-01
## theta[89] 2.092085e-01 2.289566e-01 2.503440e-01 2.908944e-01
## theta[90] 1.188138e-01 1.436403e-01 1.748369e-01 2.361034e-01
## theta[91] 2.574685e-01 2.701474e-01 2.822476e-01 3.068953e-01
## theta[92] 2.360775e-01 2.481980e-01 2.611757e-01 2.858127e-01
## theta[93] 1.087313e-01 1.346797e-01 1.686846e-01 2.485051e-01
## theta[94] 9.320697e-02 1.205865e-01 1.558437e-01 2.360749e-01
## theta[95] 2.111747e-01 2.386853e-01 2.668696e-01 3.222419e-01
## theta[96] 1.914471e-01 2.166153e-01 2.400764e-01 2.918626e-01
## theta[97] 2.131199e-01 2.264781e-01 2.404271e-01 2.695283e-01
## theta[98] 2.294149e-01 2.549474e-01 2.803906e-01 3.352583e-01
## theta[99] 2.602546e-01 2.782331e-01 2.981924e-01 3.286701e-01
## theta[100] 2.648099e-01 2.763492e-01 2.873119e-01 3.099285e-01
## theta[101] 2.384839e-01 2.609132e-01 2.833699e-01 3.312017e-01
## theta[102] 2.221923e-01 2.377701e-01 2.539694e-01 2.894373e-01
## theta[103] 1.917327e-01 2.030056e-01 2.156737e-01 2.375412e-01
## theta[104] 2.309601e-01 2.442565e-01 2.565895e-01 2.823792e-01
## theta[105] 1.980209e-01 2.137485e-01 2.290790e-01 2.590980e-01
## theta[106] 1.940028e-01 2.134213e-01 2.343083e-01 2.747292e-01
## theta[107] 2.239366e-01 2.528877e-01 2.851251e-01 3.506534e-01
## theta[108] 9.413692e-02 1.227264e-01 1.543336e-01 2.216826e-01
## theta[109] 2.375505e-01 2.622832e-01 2.901419e-01 3.386542e-01
## theta[110] 1.970912e-01 2.157694e-01 2.364462e-01 2.784773e-01
## theta[111] 1.920297e-01 2.105813e-01 2.292733e-01 2.682350e-01
## theta[112] 2.582927e-01 2.701143e-01 2.840765e-01 3.066652e-01
## theta[113] 2.106934e-01 2.312412e-01 2.504437e-01 2.891321e-01
## theta[114] 2.389482e-01 2.549613e-01 2.690625e-01 2.988345e-01
## theta[115] 2.066663e-01 2.270429e-01 2.486011e-01 2.912593e-01
## theta[116] 2.027490e-01 2.158363e-01 2.287114e-01 2.530472e-01
## theta[117] 2.239063e-01 2.367116e-01 2.504203e-01 2.797814e-01
## theta[118] 9.244595e-02 1.227819e-01 1.569819e-01 2.244198e-01
## theta[119] 1.023026e-01 1.297333e-01 1.624005e-01 2.353133e-01
## theta[120] 2.176303e-01 2.307271e-01 2.441179e-01 2.678766e-01
## theta[121] 1.999806e-01 2.212989e-01 2.423435e-01 2.892361e-01
## theta[122] 8.916871e-02 1.181754e-01 1.549068e-01 2.268229e-01
## theta[123] 2.088390e-01 2.294530e-01 2.510679e-01 2.987604e-01
## theta[124] 2.435078e-01 2.663599e-01 2.883834e-01 3.344033e-01
## theta[125] 1.110669e-01 1.332354e-01 1.597786e-01 2.099724e-01
## theta[126] 1.731390e-01 1.918264e-01 2.127462e-01 2.498252e-01
## theta[127] 1.068221e-01 1.332600e-01 1.670894e-01 2.344061e-01
## theta[128] 1.064644e-01 1.343413e-01 1.643548e-01 2.338066e-01
## theta[129] 2.058820e-01 2.358944e-01 2.668554e-01 3.376896e-01
## theta[130] 2.115699e-01 2.369695e-01 2.669308e-01 3.353913e-01
## theta[131] 2.432968e-01 2.570783e-01 2.724179e-01 2.977890e-01
## theta[132] 1.962155e-01 2.107011e-01 2.259609e-01 2.559299e-01
## theta[133] 2.563044e-01 2.688210e-01 2.810953e-01 3.023621e-01
## theta[134] 9.254056e-02 1.126499e-01 1.357719e-01 1.870368e-01
## theta[135] 8.925136e-02 1.195741e-01 1.534174e-01 2.346545e-01
## theta[136] 3.094163e-01 3.215880e-01 3.340325e-01 3.632338e-01
## theta[137] 2.329527e-01 2.448500e-01 2.569923e-01 2.793550e-01
## theta[138] 2.463795e-01 2.669644e-01 2.881801e-01 3.291656e-01
## theta[139] 9.670724e-02 1.245983e-01 1.554320e-01 2.296028e-01
## theta[140] 2.540836e-01 2.665413e-01 2.792178e-01 3.021769e-01
## theta[141] 2.304842e-01 2.539033e-01 2.778203e-01 3.216617e-01
## theta[142] 2.461471e-01 2.603086e-01 2.731789e-01 2.979980e-01
## theta[143] 2.828149e-01 2.940167e-01 3.054130e-01 3.307761e-01
## theta[144] 2.512914e-01 2.623724e-01 2.748269e-01 2.972692e-01
## theta[145] 2.118721e-01 2.344165e-01 2.569654e-01 2.982206e-01
## theta[146] 1.955747e-01 2.069905e-01 2.185949e-01 2.409093e-01
## theta[147] 2.440079e-01 2.581999e-01 2.732662e-01 2.999634e-01
## theta[148] 2.943847e-01 3.086170e-01 3.234636e-01 3.516107e-01
## theta[149] 2.384445e-01 2.504039e-01 2.625885e-01 2.858611e-01
## theta[150] 1.085505e-01 1.344167e-01 1.678410e-01 2.422640e-01
## theta[151] 2.125765e-01 2.410882e-01 2.709200e-01 3.279858e-01
## theta[152] 1.098929e-01 1.388996e-01 1.747911e-01 2.459273e-01
## theta[153] 1.231321e-01 1.477907e-01 1.758048e-01 2.410077e-01
## theta[154] 1.034250e-01 1.336008e-01 1.680144e-01 2.488838e-01
## theta[155] 1.098317e-01 1.368669e-01 1.678912e-01 2.477863e-01
## theta[156] 2.216604e-01 2.334007e-01 2.457646e-01 2.672808e-01
## theta[157] 2.120334e-01 2.259359e-01 2.401176e-01 2.674444e-01
## theta[158] 2.190105e-01 2.328503e-01 2.475002e-01 2.757280e-01
## theta[159] 9.248489e-02 1.212520e-01 1.503269e-01 2.231793e-01
## theta[160] 2.242859e-01 2.430631e-01 2.618428e-01 2.946566e-01
## theta[161] 9.217676e-02 1.213212e-01 1.529243e-01 2.236822e-01
## theta[162] 1.326531e-01 1.569046e-01 1.842495e-01 2.404498e-01
## theta[163] 8.281746e-02 1.068454e-01 1.369045e-01 2.060667e-01
## theta[164] 2.381931e-01 2.584454e-01 2.804476e-01 3.214520e-01
## theta[165] 2.488178e-01 2.694571e-01 2.904033e-01 3.304880e-01
## theta[166] 2.027718e-01 2.272325e-01 2.546775e-01 3.070864e-01
## theta[167] 2.707513e-01 2.818701e-01 2.933906e-01 3.145915e-01
## theta[168] 2.385347e-01 2.529896e-01 2.676330e-01 2.964960e-01
## theta[169] 2.655432e-01 2.799939e-01 2.949693e-01 3.245335e-01
## theta[170] 1.883065e-01 2.063016e-01 2.234089e-01 2.562786e-01
## theta[171] 8.857218e-02 1.167472e-01 1.465316e-01 2.145143e-01
## theta[172] 8.883572e-02 1.081678e-01 1.295670e-01 1.735431e-01
## theta[173] 1.759280e-01 1.948333e-01 2.144175e-01 2.580836e-01
## theta[174] 2.564934e-01 2.673111e-01 2.784742e-01 3.001905e-01
## theta[175] 2.704341e-01 2.841528e-01 2.988603e-01 3.276355e-01
## theta[176] 2.260771e-01 2.529632e-01 2.774774e-01 3.410486e-01
## theta[177] 2.471449e-01 2.649899e-01 2.843482e-01 3.198061e-01
## theta[178] 2.290847e-01 2.510199e-01 2.726688e-01 3.170231e-01
## theta[179] 2.488753e-01 2.620388e-01 2.758461e-01 3.027709e-01
## theta[180] 1.774336e-01 2.045904e-01 2.312921e-01 2.863118e-01
## theta[181] 2.230235e-01 2.385143e-01 2.557525e-01 2.871577e-01
## theta[182] 2.651035e-01 2.767198e-01 2.893199e-01 3.139114e-01
## theta[183] 9.141580e-02 1.206893e-01 1.560826e-01 2.325754e-01
## theta[184] 8.962304e-02 1.167893e-01 1.458552e-01 2.176891e-01
## theta[185] 2.770479e-01 2.904837e-01 3.062752e-01 3.335347e-01
## theta[186] 2.206676e-01 2.372713e-01 2.541927e-01 2.912836e-01
## theta[187] 8.708484e-02 1.173871e-01 1.513953e-01 2.178262e-01
## theta[188] 1.043977e-01 1.323863e-01 1.636385e-01 2.299870e-01
## theta[189] 8.908322e-02 1.176961e-01 1.487338e-01 2.188045e-01
## theta[190] 1.036510e-01 1.334128e-01 1.669082e-01 2.446403e-01
## theta[191] 1.792545e-01 1.936778e-01 2.103060e-01 2.419408e-01
## theta[192] 2.188124e-01 2.385318e-01 2.569564e-01 2.925191e-01
## theta[193] 1.184751e-01 1.441082e-01 1.703947e-01 2.287177e-01
## theta[194] 8.709102e-02 1.101838e-01 1.355706e-01 1.887118e-01
## theta[195] 8.757599e-02 1.157771e-01 1.492077e-01 2.334317e-01
## theta[196] 9.569138e-02 1.245142e-01 1.549035e-01 2.263106e-01
## theta[197] 1.456651e-01 1.676989e-01 1.924620e-01 2.478467e-01
## theta[198] 8.747328e-02 1.189759e-01 1.532700e-01 2.291024e-01
## theta[199] 8.519244e-02 1.033696e-01 1.230859e-01 1.691272e-01
## theta[200] 2.089127e-01 2.336694e-01 2.598300e-01 3.116827e-01
## theta[201] 2.091197e-01 2.211046e-01 2.326990e-01 2.562960e-01
## theta[202] 2.199690e-01 2.325363e-01 2.438443e-01 2.684464e-01
## theta[203] 2.463028e-01 2.587439e-01 2.707066e-01 2.954796e-01
## theta[204] 2.110955e-01 2.264249e-01 2.413675e-01 2.738009e-01
## theta[205] 2.523015e-01 2.645862e-01 2.766728e-01 3.010205e-01
## theta[206] 1.222611e-01 1.528055e-01 1.882166e-01 2.779323e-01
## theta[207] 2.167003e-01 2.277301e-01 2.389979e-01 2.603323e-01
## theta[208] 1.552491e-01 1.764033e-01 2.011188e-01 2.528872e-01
## theta[209] 2.362913e-01 2.571202e-01 2.776757e-01 3.210231e-01
## theta[210] 8.504943e-02 1.125085e-01 1.473495e-01 2.175344e-01
## theta[211] 2.071844e-01 2.335660e-01 2.615164e-01 3.164657e-01
## theta[212] 2.153541e-01 2.391898e-01 2.664734e-01 3.178608e-01
## theta[213] 2.122769e-01 2.365267e-01 2.600238e-01 3.084159e-01
## theta[214] 2.547576e-01 2.667920e-01 2.786112e-01 3.010332e-01
## theta[215] 9.446276e-02 1.220485e-01 1.548619e-01 2.280702e-01
## theta[216] 7.825738e-02 1.013965e-01 1.281779e-01 1.936385e-01
## theta[217] 8.895235e-02 1.171493e-01 1.500975e-01 2.249453e-01
## theta[218] 2.726808e-01 2.892629e-01 3.075833e-01 3.439359e-01
## theta[219] 8.582261e-02 1.109811e-01 1.430406e-01 2.157955e-01
## theta[220] 8.801114e-02 1.169172e-01 1.479841e-01 2.197698e-01
## theta[221] 2.236326e-01 2.353792e-01 2.462412e-01 2.675904e-01
## theta[222] 9.309025e-02 1.230197e-01 1.529224e-01 2.344371e-01
## theta[223] 9.196014e-02 1.173693e-01 1.480888e-01 2.106644e-01
## theta[224] 8.616309e-02 1.145398e-01 1.448841e-01 2.272623e-01
## theta[225] 9.186605e-02 1.195837e-01 1.574327e-01 2.317420e-01
## theta[226] 2.414886e-01 2.706387e-01 2.979165e-01 3.513193e-01
## theta[227] 9.351295e-02 1.213179e-01 1.541231e-01 2.316837e-01
## theta[228] 2.136157e-01 2.244518e-01 2.365380e-01 2.593529e-01
## theta[229] 9.061962e-02 1.188444e-01 1.527264e-01 2.180950e-01
## theta[230] 2.183635e-01 2.324209e-01 2.461007e-01 2.717644e-01
## theta[231] 1.060328e-01 1.318428e-01 1.604513e-01 2.295631e-01
## theta[232] 2.728927e-01 2.841799e-01 2.965011e-01 3.240987e-01
## theta[233] 2.283371e-01 2.441961e-01 2.589145e-01 2.900935e-01
## theta[234] 2.364067e-01 2.477135e-01 2.591646e-01 2.825120e-01
## theta[235] 1.959924e-01 2.146491e-01 2.310849e-01 2.659576e-01
## theta[236] 2.119993e-01 2.330267e-01 2.544144e-01 3.021620e-01
## theta[237] 2.091708e-01 2.271588e-01 2.459057e-01 2.878815e-01
## theta[238] 2.357804e-01 2.522698e-01 2.694475e-01 3.045227e-01
## theta[239] 2.475597e-01 2.723833e-01 2.994670e-01 3.535497e-01
## theta[240] 2.076470e-01 2.273368e-01 2.477457e-01 2.860985e-01
## theta[241] 2.410483e-01 2.525240e-01 2.643040e-01 2.863539e-01
## theta[242] 2.405049e-01 2.629225e-01 2.875638e-01 3.301329e-01
## theta[243] 2.595202e-01 2.779081e-01 2.980678e-01 3.365827e-01
## theta[244] 2.501089e-01 2.612383e-01 2.732172e-01 2.991614e-01
## theta[245] 2.755060e-01 2.875372e-01 3.000703e-01 3.252372e-01
## theta[246] 1.124989e-01 1.446398e-01 1.812691e-01 2.608416e-01
## theta[247] 9.442018e-02 1.193129e-01 1.531156e-01 2.211317e-01
## theta[248] 2.254524e-01 2.481507e-01 2.706130e-01 3.197639e-01
## theta[249] 2.802306e-01 2.932479e-01 3.069292e-01 3.326677e-01
## theta[250] 2.873958e-01 3.018080e-01 3.167901e-01 3.482267e-01
## theta[251] 8.844331e-02 1.147313e-01 1.444929e-01 2.158422e-01
## theta[252] 2.319588e-01 2.500655e-01 2.684500e-01 3.082731e-01
## theta[253] 2.871167e-01 2.987650e-01 3.107781e-01 3.339720e-01
## theta[254] 2.441916e-01 2.560565e-01 2.669669e-01 2.915896e-01
## theta[255] 2.168534e-01 2.312347e-01 2.461149e-01 2.750847e-01
## theta[256] 2.543970e-01 2.642114e-01 2.756508e-01 2.997910e-01
## theta[257] 2.675069e-01 2.795870e-01 2.923865e-01 3.174919e-01
## theta[258] 2.332860e-01 2.638544e-01 2.943624e-01 3.611713e-01
## theta[259] 8.819883e-02 1.195232e-01 1.516000e-01 2.239317e-01
## theta[260] 2.962930e-01 3.080187e-01 3.194523e-01 3.424700e-01
## theta[261] 1.204906e-01 1.529695e-01 1.867875e-01 2.644323e-01
## theta[262] 1.966154e-01 2.125181e-01 2.280467e-01 2.621407e-01
## theta[263] 2.331321e-01 2.453466e-01 2.584080e-01 2.799994e-01
## theta[264] 2.052139e-01 2.204616e-01 2.378777e-01 2.709532e-01
## theta[265] 2.399245e-01 2.547154e-01 2.708213e-01 3.004694e-01
## theta[266] 2.784189e-01 2.917873e-01 3.052744e-01 3.344154e-01
## theta[267] 2.288723e-01 2.550431e-01 2.842046e-01 3.451721e-01
## theta[268] 1.090514e-01 1.334723e-01 1.623743e-01 2.216755e-01
## theta[269] 2.375420e-01 2.605886e-01 2.846698e-01 3.278835e-01
## theta[270] 2.646668e-01 2.820266e-01 2.981799e-01 3.300700e-01
## theta[271] 2.271534e-01 2.441983e-01 2.600298e-01 2.967094e-01
## theta[272] 1.997342e-01 2.200699e-01 2.393958e-01 2.776089e-01
## theta[273] 2.125577e-01 2.329493e-01 2.537679e-01 2.947574e-01
## theta[274] 2.671827e-01 2.824946e-01 2.980316e-01 3.312891e-01
## theta[275] 8.921598e-02 1.179123e-01 1.510346e-01 2.272545e-01
## theta[276] 1.951332e-01 2.139505e-01 2.333897e-01 2.710946e-01
## theta[277] 9.232142e-02 1.188743e-01 1.520030e-01 2.212179e-01
## theta[278] 1.355340e-01 1.608708e-01 1.909465e-01 2.466767e-01
## theta[279] 9.213783e-02 1.189431e-01 1.529513e-01 2.327094e-01
## theta[280] 2.078732e-01 2.193416e-01 2.316741e-01 2.540549e-01
## theta[281] 2.315943e-01 2.508677e-01 2.686823e-01 3.078382e-01
## theta[282] 9.100690e-02 1.204925e-01 1.534995e-01 2.377119e-01
## theta[283] 2.182066e-01 2.284093e-01 2.398495e-01 2.613219e-01
## theta[284] 9.273787e-02 1.218579e-01 1.550026e-01 2.308132e-01
## theta[285] 2.704964e-01 2.829721e-01 2.954589e-01 3.174107e-01
## theta[286] 7.962539e-02 9.800273e-02 1.176805e-01 1.652636e-01
## theta[287] 2.106964e-01 2.294615e-01 2.476202e-01 2.851397e-01
## theta[288] 2.476593e-01 2.689653e-01 2.925047e-01 3.364560e-01
## theta[289] 9.408488e-02 1.213353e-01 1.570314e-01 2.279890e-01
## theta[290] 2.645945e-01 2.760235e-01 2.876059e-01 3.103213e-01
## theta[291] 1.557773e-01 1.791882e-01 2.034615e-01 2.557316e-01
## theta[292] 2.224051e-01 2.459972e-01 2.710172e-01 3.188201e-01
## theta[293] 1.928548e-01 2.197797e-01 2.480953e-01 3.056866e-01
## theta[294] 2.334963e-01 2.505355e-01 2.670771e-01 2.999564e-01
## theta[295] 2.267162e-01 2.423838e-01 2.590497e-01 2.892945e-01
## theta[296] 9.426958e-02 1.223322e-01 1.544857e-01 2.330287e-01
## theta[297] 2.694483e-01 2.816025e-01 2.930753e-01 3.159812e-01
## theta[298] 2.432391e-01 2.585557e-01 2.746589e-01 3.074638e-01
## theta[299] 2.088038e-01 2.265501e-01 2.451261e-01 2.797292e-01
## theta[300] 2.024006e-01 2.180710e-01 2.352417e-01 2.720106e-01
## theta[301] 2.587744e-01 2.743806e-01 2.903336e-01 3.220497e-01
## theta[302] 2.117966e-01 2.376273e-01 2.656856e-01 3.286762e-01
## theta[303] 2.188053e-01 2.458663e-01 2.769120e-01 3.358482e-01
## theta[304] 9.216480e-02 1.216976e-01 1.500604e-01 2.256381e-01
## theta[305] 2.043235e-01 2.227635e-01 2.401593e-01 2.757668e-01
## theta[306] 2.244516e-01 2.352819e-01 2.466573e-01 2.689862e-01
## theta[307] 1.815610e-01 2.031127e-01 2.218556e-01 2.660198e-01
## theta[308] 1.414590e-01 1.695435e-01 1.967417e-01 2.564117e-01
## theta[309] 2.223840e-01 2.367119e-01 2.508636e-01 2.825037e-01
## theta[310] 2.718266e-01 2.837573e-01 2.962856e-01 3.216821e-01
## theta[311] 9.640425e-02 1.171004e-01 1.407679e-01 1.881813e-01
## theta[312] 2.196120e-01 2.424294e-01 2.637551e-01 3.121944e-01
## theta[313] 2.264423e-01 2.441889e-01 2.631850e-01 3.037151e-01
## theta[314] 8.596958e-02 1.133879e-01 1.415607e-01 2.112139e-01
## theta[315] 1.072753e-01 1.370315e-01 1.682519e-01 2.423692e-01
## theta[316] 2.204451e-01 2.529711e-01 2.874375e-01 3.474919e-01
## theta[317] 2.656498e-01 2.803319e-01 2.957485e-01 3.274030e-01
## theta[318] 2.323273e-01 2.458630e-01 2.598995e-01 2.869175e-01
## theta[319] 2.416488e-01 2.604538e-01 2.788876e-01 3.192540e-01
## theta[320] 9.590887e-02 1.251703e-01 1.564453e-01 2.297870e-01
## theta[321] 1.068027e-01 1.379433e-01 1.719028e-01 2.419400e-01
## theta[322] 9.987436e-02 1.275903e-01 1.581668e-01 2.331675e-01
## theta[323] 2.230445e-01 2.418180e-01 2.621052e-01 2.983894e-01
## theta[324] 9.101741e-02 1.187643e-01 1.515287e-01 2.249810e-01
## theta[325] 9.493765e-02 1.219978e-01 1.503427e-01 2.267933e-01
## theta[326] 2.052042e-01 2.337555e-01 2.643800e-01 3.270508e-01
## theta[327] 8.953492e-02 1.199029e-01 1.508794e-01 2.276621e-01
## theta[328] 2.112604e-01 2.361438e-01 2.634105e-01 3.179037e-01
## theta[329] 2.387349e-01 2.575332e-01 2.764149e-01 3.193145e-01
## theta[330] 1.092525e-01 1.386710e-01 1.746720e-01 2.492295e-01
## theta[331] 2.459530e-01 2.573815e-01 2.693817e-01 2.916369e-01
## theta[332] 2.189832e-01 2.337058e-01 2.484763e-01 2.791188e-01
## theta[333] 2.133900e-01 2.276012e-01 2.410570e-01 2.716949e-01
## theta[334] 2.576580e-01 2.697528e-01 2.822964e-01 3.063146e-01
## theta[335] 9.080512e-02 1.185083e-01 1.545667e-01 2.228319e-01
## theta[336] 9.672751e-02 1.253714e-01 1.584124e-01 2.366839e-01
## theta[337] 2.025471e-01 2.286285e-01 2.548266e-01 3.014357e-01
## theta[338] 9.321036e-02 1.228423e-01 1.555413e-01 2.364539e-01
## theta[339] 2.019524e-01 2.183664e-01 2.364593e-01 2.676094e-01
## theta[340] 1.926647e-01 2.066545e-01 2.201396e-01 2.483790e-01
## theta[341] 2.495368e-01 2.679524e-01 2.865512e-01 3.233548e-01
## theta[342] 2.569936e-01 2.702630e-01 2.840279e-01 3.087189e-01
## theta[343] 2.705470e-01 2.840692e-01 2.976250e-01 3.214930e-01
## theta[344] 2.190926e-01 2.423936e-01 2.673190e-01 3.167858e-01
## theta[345] 8.996083e-02 1.083542e-01 1.269795e-01 1.733436e-01
## theta[346] 2.242676e-01 2.356401e-01 2.484637e-01 2.706405e-01
## theta[347] 1.970479e-01 2.148809e-01 2.329587e-01 2.655629e-01
## theta[348] 9.458287e-02 1.226731e-01 1.536361e-01 2.266786e-01
## theta[349] 2.632749e-01 2.774135e-01 2.930187e-01 3.195345e-01
## theta[350] 2.343036e-01 2.459963e-01 2.590064e-01 2.864593e-01
## theta[351] 1.088857e-01 1.345930e-01 1.640558e-01 2.355745e-01
## theta[352] 2.032977e-01 2.301024e-01 2.629949e-01 3.263499e-01
## theta[353] 1.979524e-01 2.240642e-01 2.534463e-01 3.185055e-01
## theta[354] 2.455379e-01 2.571453e-01 2.684748e-01 2.922063e-01
## theta[355] 2.332560e-01 2.624689e-01 2.933685e-01 3.592389e-01
## theta[356] 2.164743e-01 2.391645e-01 2.616721e-01 3.083936e-01
## theta[357] 1.229735e-01 1.518670e-01 1.853451e-01 2.663347e-01
## theta[358] 2.516900e-01 2.689679e-01 2.859647e-01 3.209914e-01
## theta[359] 9.527223e-02 1.237903e-01 1.569441e-01 2.255343e-01
## theta[360] 1.934665e-01 2.157246e-01 2.390784e-01 2.863092e-01
## theta[361] 2.240569e-01 2.546547e-01 2.855757e-01 3.481660e-01
## theta[362] 1.820930e-01 1.992999e-01 2.202217e-01 2.587835e-01
## theta[363] 8.948749e-02 1.182067e-01 1.529517e-01 2.242681e-01
## theta[364] 1.009849e-01 1.186630e-01 1.394391e-01 1.801742e-01
## theta[365] 2.701943e-01 2.818685e-01 2.939409e-01 3.174216e-01
## theta[366] 2.143673e-01 2.339353e-01 2.536580e-01 2.895211e-01
## theta[367] 2.422081e-01 2.537802e-01 2.645737e-01 2.855729e-01
## theta[368] 2.734921e-01 2.857349e-01 2.986128e-01 3.218654e-01
## theta[369] 8.256750e-02 1.015296e-01 1.218509e-01 1.670962e-01
## theta[370] 2.447734e-01 2.548020e-01 2.655413e-01 2.859725e-01
## theta[371] 2.032150e-01 2.186423e-01 2.368766e-01 2.693313e-01
## theta[372] 2.682141e-01 2.788424e-01 2.899536e-01 3.125267e-01
## theta[373] 2.686581e-01 2.899138e-01 3.128927e-01 3.599083e-01
## theta[374] 2.176889e-01 2.397438e-01 2.633980e-01 3.113587e-01
## theta[375] 1.001255e-01 1.312648e-01 1.626159e-01 2.299150e-01
## theta[376] 2.313638e-01 2.469376e-01 2.618272e-01 2.923117e-01
## theta[377] 7.178899e-02 9.612777e-02 1.247588e-01 1.930157e-01
## theta[378] 2.526037e-01 2.668206e-01 2.806387e-01 3.116387e-01
## theta[379] 1.516625e-01 1.790402e-01 2.090805e-01 2.639480e-01
## theta[380] 9.159114e-02 1.160873e-01 1.434343e-01 2.094569e-01
## theta[381] 9.214661e-02 1.197256e-01 1.503164e-01 2.187060e-01
## theta[382] 1.989837e-01 2.212337e-01 2.431181e-01 2.875370e-01
## theta[383] 8.419866e-02 1.110636e-01 1.431498e-01 2.085340e-01
## theta[384] 1.038884e-01 1.231417e-01 1.466609e-01 1.905702e-01
## theta[385] 2.178092e-01 2.438140e-01 2.726709e-01 3.225929e-01
## theta[386] 2.367790e-01 2.498626e-01 2.633160e-01 2.908505e-01
## theta[387] 1.120050e-01 1.330488e-01 1.573849e-01 2.093295e-01
## theta[388] 9.341892e-02 1.227750e-01 1.544736e-01 2.311096e-01
## theta[389] 1.020229e-01 1.310798e-01 1.631091e-01 2.429129e-01
## theta[390] 2.521825e-01 2.637566e-01 2.761756e-01 3.037409e-01
## theta[391] 9.331474e-02 1.224080e-01 1.536704e-01 2.264514e-01
## theta[392] 1.010265e-01 1.264460e-01 1.528916e-01 2.214849e-01
## theta[393] 9.653849e-02 1.246201e-01 1.540843e-01 2.291012e-01
## theta[394] 2.431909e-01 2.578191e-01 2.725950e-01 3.022178e-01
## theta[395] 8.206251e-02 1.086851e-01 1.384110e-01 2.084457e-01
## theta[396] 2.119527e-01 2.241563e-01 2.374319e-01 2.622768e-01
## theta[397] 1.700421e-01 1.898793e-01 2.124225e-01 2.573357e-01
## theta[398] 1.780207e-01 1.934070e-01 2.084896e-01 2.412139e-01
## theta[399] 8.588523e-02 1.141238e-01 1.456085e-01 2.202724e-01
## theta[400] 2.338650e-01 2.576516e-01 2.819253e-01 3.328203e-01
## theta[401] 2.361519e-01 2.508358e-01 2.655000e-01 2.946200e-01
## theta[402] 2.043524e-01 2.236347e-01 2.435689e-01 2.826491e-01
## theta[403] 2.189267e-01 2.410075e-01 2.615992e-01 3.029136e-01
## theta[404] 8.869055e-02 1.143848e-01 1.441714e-01 2.158682e-01
## theta[405] 2.558831e-01 2.671731e-01 2.791428e-01 3.002393e-01
## theta[406] 2.447568e-01 2.545859e-01 2.674334e-01 2.902157e-01
## theta[407] 2.405567e-01 2.527199e-01 2.647287e-01 2.905153e-01
## theta[408] 1.597855e-01 1.843209e-01 2.133930e-01 2.824081e-01
## theta[409] 2.344427e-01 2.613461e-01 2.908233e-01 3.532495e-01
## theta[410] 2.093606e-01 2.394623e-01 2.696472e-01 3.296185e-01
## theta[411] 1.203531e-01 1.496361e-01 1.827995e-01 2.613553e-01
## theta[412] 2.418062e-01 2.516818e-01 2.634385e-01 2.845978e-01
## theta[413] 2.283114e-01 2.453527e-01 2.642977e-01 3.012685e-01
## theta[414] 2.739267e-01 2.897980e-01 3.043114e-01 3.339806e-01
## theta[415] 2.349904e-01 2.545745e-01 2.748652e-01 3.109033e-01
## theta[416] 1.040325e-01 1.330949e-01 1.653732e-01 2.375171e-01
## theta[417] 2.300566e-01 2.434861e-01 2.573883e-01 2.847016e-01
## theta[418] 2.293538e-01 2.457187e-01 2.626766e-01 2.978859e-01
## theta[419] 1.979095e-01 2.203626e-01 2.456485e-01 2.916825e-01
## theta[420] 2.064375e-01 2.322683e-01 2.558590e-01 3.074485e-01
## theta[421] 7.915388e-02 1.030964e-01 1.279196e-01 1.834762e-01
## theta[422] 2.270112e-01 2.384503e-01 2.505667e-01 2.748251e-01
## theta[423] 9.335413e-02 1.164062e-01 1.436326e-01 1.960816e-01
## theta[424] 2.957145e-01 3.092432e-01 3.251194e-01 3.544413e-01
## theta[425] 9.353299e-02 1.169946e-01 1.465949e-01 2.083433e-01
## theta[426] 2.067133e-01 2.226607e-01 2.401397e-01 2.757642e-01
## theta[427] 9.000431e-02 1.131133e-01 1.349671e-01 1.838454e-01
## theta[428] 9.637267e-02 1.222743e-01 1.535911e-01 2.186312e-01
## theta[429] 2.132516e-01 2.252944e-01 2.381590e-01 2.591804e-01
## theta[430] 9.187014e-02 1.188617e-01 1.486729e-01 2.125407e-01
## theta[431] 1.072405e-01 1.371882e-01 1.690615e-01 2.509602e-01
## theta[432] 9.528795e-02 1.231059e-01 1.551654e-01 2.280715e-01
## theta[433] 8.755196e-02 1.116196e-01 1.358609e-01 1.946611e-01
## theta[434] 9.143459e-02 1.170596e-01 1.451411e-01 2.107235e-01
## theta[435] 9.228361e-02 1.196621e-01 1.525419e-01 2.272179e-01
## theta[436] 2.320129e-01 2.557919e-01 2.826238e-01 3.379102e-01
## theta[437] 1.096348e-01 1.388968e-01 1.713401e-01 2.515176e-01
## theta[438] 2.091539e-01 2.345842e-01 2.613346e-01 3.125191e-01
## theta[439] 8.733481e-02 1.135461e-01 1.452632e-01 2.190471e-01
## theta[440] 2.054427e-01 2.187111e-01 2.333221e-01 2.599000e-01
## theta[441] 2.336620e-01 2.471276e-01 2.612111e-01 2.887504e-01
## theta[442] 2.439106e-01 2.566229e-01 2.688198e-01 2.915081e-01
## theta[443] 9.555239e-02 1.242110e-01 1.598586e-01 2.416614e-01
## theta[444] 2.328750e-01 2.577670e-01 2.867955e-01 3.416132e-01
## theta[445] 2.299911e-01 2.399250e-01 2.522517e-01 2.759142e-01
## theta[446] 1.496132e-01 1.782470e-01 2.104088e-01 2.818155e-01
## theta[447] 2.344951e-01 2.534944e-01 2.735627e-01 3.052121e-01
## theta[448] 2.062393e-01 2.274724e-01 2.505269e-01 2.852863e-01
## theta[449] 2.392126e-01 2.495514e-01 2.609876e-01 2.792569e-01
## theta[450] 2.494157e-01 2.645941e-01 2.806179e-01 3.080407e-01
## theta[451] 7.925402e-02 9.935192e-02 1.202616e-01 1.639630e-01
## theta[452] 2.144131e-01 2.437968e-01 2.726474e-01 3.311118e-01
## theta[453] 2.073050e-01 2.228750e-01 2.385668e-01 2.712273e-01
## theta[454] 2.956162e-01 3.080974e-01 3.203792e-01 3.420431e-01
## theta[455] 8.644431e-02 1.074384e-01 1.332887e-01 1.874244e-01
## theta[456] 9.484931e-02 1.229211e-01 1.533933e-01 2.308756e-01
## theta[457] 1.133307e-01 1.411285e-01 1.724575e-01 2.501522e-01
## theta[458] 9.744071e-02 1.253514e-01 1.585212e-01 2.392053e-01
## theta[459] 3.040191e-01 3.171299e-01 3.318582e-01 3.625465e-01
## theta[460] 8.927662e-02 1.089843e-01 1.337285e-01 1.842730e-01
## theta[461] 9.213767e-02 1.221008e-01 1.565014e-01 2.365180e-01
## theta[462] 2.216333e-01 2.380356e-01 2.550280e-01 2.909104e-01
## theta[463] 1.896836e-01 2.023664e-01 2.154944e-01 2.401749e-01
## theta[464] 9.305099e-02 1.193022e-01 1.484864e-01 2.275711e-01
## theta[465] 2.034452e-01 2.254544e-01 2.455278e-01 2.899968e-01
## theta[466] 2.512356e-01 2.652738e-01 2.816630e-01 3.094918e-01
## theta[467] 9.697595e-02 1.230182e-01 1.515993e-01 2.187251e-01
## theta[468] 8.849802e-02 1.060484e-01 1.245899e-01 1.693481e-01
## theta[469] 2.147983e-01 2.315314e-01 2.476800e-01 2.786685e-01
## theta[470] 2.247575e-01 2.411458e-01 2.581390e-01 2.953597e-01
## theta[471] 2.831510e-01 2.965744e-01 3.100635e-01 3.378544e-01
## theta[472] 8.865339e-02 1.167044e-01 1.491540e-01 2.260133e-01
## theta[473] 2.412609e-01 2.566438e-01 2.740853e-01 3.048236e-01
## theta[474] 2.850498e-01 3.017531e-01 3.188709e-01 3.458367e-01
## theta[475] 8.605166e-02 1.131050e-01 1.446013e-01 2.170861e-01
## theta[476] 1.470871e-01 1.729184e-01 2.000848e-01 2.630569e-01
## theta[477] 2.436561e-01 2.580349e-01 2.732179e-01 3.030203e-01
## theta[478] 2.141248e-01 2.368743e-01 2.607432e-01 3.033701e-01
## theta[479] 1.162200e-01 1.392910e-01 1.655382e-01 2.275780e-01
## theta[480] 2.864072e-01 3.003341e-01 3.134290e-01 3.388958e-01
## theta[481] 2.077898e-01 2.210945e-01 2.357452e-01 2.607973e-01
## theta[482] 1.398658e-01 1.620308e-01 1.868839e-01 2.401581e-01
## theta[483] 2.257036e-01 2.421952e-01 2.587044e-01 2.908743e-01
## theta[484] 2.090873e-01 2.298802e-01 2.534769e-01 3.039669e-01
## theta[485] 1.192529e-01 1.474534e-01 1.829757e-01 2.652843e-01
## theta[486] 2.719837e-01 2.836892e-01 2.959087e-01 3.209984e-01
## theta[487] 2.270923e-01 2.481751e-01 2.693910e-01 3.159366e-01
## theta[488] 1.674881e-01 1.909294e-01 2.104363e-01 2.561150e-01
## theta[489] 2.068514e-01 2.272857e-01 2.472391e-01 2.858662e-01
## theta[490] 2.323159e-01 2.485266e-01 2.645961e-01 2.973044e-01
## theta[491] 9.900171e-02 1.302645e-01 1.665037e-01 2.362972e-01
## theta[492] 2.130732e-01 2.271315e-01 2.425191e-01 2.714411e-01
## theta[493] 9.313316e-02 1.196783e-01 1.488882e-01 2.259812e-01
## theta[494] 2.338852e-01 2.466710e-01 2.604605e-01 2.881965e-01
## theta[495] 7.914799e-02 1.024184e-01 1.290287e-01 1.888308e-01
## theta[496] 8.780536e-02 1.124866e-01 1.400781e-01 1.976622e-01
## theta[497] 2.300540e-01 2.450315e-01 2.608160e-01 2.886621e-01
## theta[498] 2.695700e-01 2.811442e-01 2.931612e-01 3.187707e-01
## theta[499] 2.234224e-01 2.382567e-01 2.534583e-01 2.854069e-01
## theta[500] 9.274574e-02 1.111607e-01 1.325165e-01 1.756971e-01
## theta[501] 8.960889e-02 1.166396e-01 1.433587e-01 2.068240e-01
## theta[502] 2.334843e-01 2.447330e-01 2.545327e-01 2.761773e-01
## theta[503] 9.065796e-02 1.164544e-01 1.470810e-01 2.129343e-01
## theta[504] 2.515195e-01 2.669535e-01 2.820565e-01 3.141521e-01
## theta[505] 9.520167e-02 1.220187e-01 1.549549e-01 2.309328e-01
## theta[506] 2.200556e-01 2.342016e-01 2.482761e-01 2.775509e-01
## theta[507] 1.193547e-01 1.474671e-01 1.825493e-01 2.603243e-01
## theta[508] 1.658714e-01 1.846777e-01 2.034225e-01 2.456198e-01
## theta[509] 2.458547e-01 2.587104e-01 2.706513e-01 2.937775e-01
## theta[510] 2.253151e-01 2.428917e-01 2.608964e-01 2.996806e-01
## theta[511] 9.726239e-02 1.243023e-01 1.537656e-01 2.230272e-01
## theta[512] 2.815779e-01 2.943762e-01 3.069456e-01 3.346286e-01
## theta[513] 2.313703e-01 2.456864e-01 2.596096e-01 2.865547e-01
## theta[514] 1.998879e-01 2.166716e-01 2.339528e-01 2.676260e-01
## theta[515] 9.229052e-02 1.210715e-01 1.529138e-01 2.226735e-01
## theta[516] 2.072795e-01 2.362223e-01 2.659171e-01 3.157506e-01
## theta[517] 1.812805e-01 2.031989e-01 2.247443e-01 2.690110e-01
## theta[518] 8.377557e-02 1.099280e-01 1.393242e-01 2.008471e-01
## theta[519] 9.194065e-02 1.223059e-01 1.589630e-01 2.302728e-01
## theta[520] 9.445616e-02 1.226629e-01 1.570583e-01 2.356620e-01
## theta[521] 2.216678e-01 2.347492e-01 2.495262e-01 2.796645e-01
## theta[522] 2.521352e-01 2.645876e-01 2.770098e-01 3.020158e-01
## theta[523] 2.835073e-01 2.994902e-01 3.139916e-01 3.454221e-01
## theta[524] 2.047407e-01 2.296614e-01 2.559437e-01 3.043138e-01
## theta[525] 2.113463e-01 2.242139e-01 2.359475e-01 2.583959e-01
## theta[526] 2.444405e-01 2.609746e-01 2.774946e-01 3.135023e-01
## theta[527] 2.638781e-01 2.754640e-01 2.872913e-01 3.117700e-01
## theta[528] 8.716437e-02 1.143189e-01 1.470115e-01 2.204403e-01
## theta[529] 2.175938e-01 2.285361e-01 2.402572e-01 2.643080e-01
## theta[530] 2.170647e-01 2.338935e-01 2.507625e-01 2.862978e-01
## theta[531] 2.554645e-01 2.682968e-01 2.811623e-01 3.069543e-01
## theta[532] 9.286746e-02 1.198098e-01 1.534266e-01 2.288507e-01
## theta[533] 9.380488e-02 1.136885e-01 1.381715e-01 1.862088e-01
## theta[534] 2.937858e-01 3.102737e-01 3.278021e-01 3.619182e-01
## theta[535] 2.095440e-01 2.334091e-01 2.622950e-01 3.207658e-01
## theta[536] 8.923111e-02 1.133764e-01 1.442643e-01 2.146552e-01
## theta[537] 2.271380e-01 2.390810e-01 2.521193e-01 2.756963e-01
## theta[538] 9.046308e-02 1.159957e-01 1.444198e-01 2.064796e-01
## theta[539] 2.401092e-01 2.532955e-01 2.677082e-01 2.953245e-01
## theta[540] 2.162873e-01 2.424149e-01 2.702643e-01 3.199251e-01
## theta[541] 1.948582e-01 2.220860e-01 2.534029e-01 3.052466e-01
## theta[542] 2.017386e-01 2.246836e-01 2.492082e-01 3.032760e-01
## theta[543] 1.947929e-01 2.175771e-01 2.426439e-01 2.915980e-01
## theta[544] 1.014237e-01 1.234347e-01 1.482820e-01 2.057430e-01
## theta[545] 2.265288e-01 2.541258e-01 2.847304e-01 3.515308e-01
## theta[546] 2.226942e-01 2.353530e-01 2.488093e-01 2.767305e-01
## theta[547] 2.226280e-01 2.534529e-01 2.849481e-01 3.476709e-01
## theta[548] 8.897810e-02 1.185209e-01 1.527139e-01 2.202949e-01
## theta[549] 1.096159e-01 1.304215e-01 1.554451e-01 2.089081e-01
## theta[550] 8.869659e-02 1.071539e-01 1.282194e-01 1.723180e-01
## theta[551] 9.326092e-02 1.240159e-01 1.546614e-01 2.280509e-01
## theta[552] 8.684292e-02 1.128111e-01 1.411141e-01 2.056368e-01
## theta[553] 2.469193e-01 2.580630e-01 2.712033e-01 2.937152e-01
## theta[554] 8.446408e-02 1.106725e-01 1.430439e-01 2.081929e-01
## theta[555] 2.328612e-01 2.534084e-01 2.762735e-01 3.200730e-01
## theta[556] 7.733788e-02 9.676889e-02 1.160933e-01 1.597926e-01
## theta[557] 2.113531e-01 2.366010e-01 2.629061e-01 3.145825e-01
## theta[558] 2.276150e-01 2.473522e-01 2.675607e-01 3.093483e-01
## theta[559] 2.051130e-01 2.285734e-01 2.535602e-01 3.041279e-01
## theta[560] 1.985321e-01 2.196472e-01 2.423997e-01 2.869756e-01
## theta[561] 9.169513e-02 1.203600e-01 1.511205e-01 2.193910e-01
## theta[562] 9.097245e-02 1.169981e-01 1.508820e-01 2.228792e-01
## theta[563] 2.524672e-01 2.665683e-01 2.827247e-01 3.107884e-01
## theta[564] 2.209005e-01 2.355610e-01 2.502368e-01 2.774635e-01
## theta[565] 2.399524e-01 2.665155e-01 2.944177e-01 3.516424e-01
## theta[566] 2.415731e-01 2.609932e-01 2.802450e-01 3.273519e-01
## theta[567] 2.471407e-01 2.637345e-01 2.811320e-01 3.131325e-01
## theta[568] 2.126139e-01 2.284702e-01 2.450325e-01 2.800094e-01
## theta[569] 2.316497e-01 2.440564e-01 2.572712e-01 2.834006e-01
## theta[570] 1.161019e-01 1.376836e-01 1.621652e-01 2.159560e-01
## theta[571] 1.078854e-01 1.349752e-01 1.697747e-01 2.435538e-01
## theta[572] 2.697778e-01 2.860475e-01 3.020083e-01 3.319673e-01
## theta[573] 1.763230e-01 2.033716e-01 2.309910e-01 2.836717e-01
## theta[574] 2.181003e-01 2.475776e-01 2.785990e-01 3.344164e-01
## theta[575] 9.308066e-02 1.212822e-01 1.525854e-01 2.353152e-01
## theta[576] 9.467834e-02 1.222508e-01 1.559055e-01 2.371301e-01
## theta[577] 2.140399e-01 2.286305e-01 2.435244e-01 2.761410e-01
## theta[578] 2.039978e-01 2.297905e-01 2.589229e-01 3.197824e-01
## theta[579] 9.425433e-02 1.234392e-01 1.559754e-01 2.271961e-01
## theta[580] 1.018390e-01 1.318985e-01 1.664795e-01 2.511463e-01
## theta[581] 2.040642e-01 2.296868e-01 2.569741e-01 3.127781e-01
## theta[582] 2.217902e-01 2.357796e-01 2.495354e-01 2.766254e-01
## theta[583] 2.367230e-01 2.557726e-01 2.749110e-01 3.124877e-01
## theta[584] 1.248545e-01 1.472555e-01 1.703591e-01 2.243819e-01
## theta[585] 2.410326e-01 2.557128e-01 2.707309e-01 2.983887e-01
## theta[586] 9.797638e-02 1.260499e-01 1.583398e-01 2.316159e-01
## theta[587] 2.403331e-01 2.576200e-01 2.750597e-01 3.095525e-01
## theta[588] 9.386340e-02 1.214038e-01 1.546066e-01 2.218022e-01
## theta[589] 2.045824e-01 2.315832e-01 2.638675e-01 3.339947e-01
## theta[590] 9.284077e-02 1.143311e-01 1.378925e-01 1.863078e-01
## theta[591] 2.869851e-01 2.977702e-01 3.086743e-01 3.309821e-01
## theta[592] 6.472857e-02 8.083873e-02 9.961482e-02 1.360440e-01
## theta[593] 2.037004e-01 2.218861e-01 2.435280e-01 2.862103e-01
## theta[594] 2.433551e-01 2.552323e-01 2.675606e-01 2.972561e-01
## theta[595] 2.362333e-01 2.551792e-01 2.732029e-01 3.103030e-01
## theta[596] 2.143440e-01 2.263787e-01 2.380580e-01 2.624866e-01
## theta[597] 1.175679e-01 1.472575e-01 1.775591e-01 2.485219e-01
## theta[598] 2.396915e-01 2.508310e-01 2.627579e-01 2.873125e-01
## theta[599] 2.536296e-01 2.652095e-01 2.759403e-01 2.982276e-01
## theta[600] 2.114528e-01 2.301351e-01 2.504937e-01 2.902357e-01
## theta[601] 2.418298e-01 2.590591e-01 2.775137e-01 3.053184e-01
## theta[602] 2.827458e-01 2.940739e-01 3.053837e-01 3.247672e-01
## theta[603] 2.210434e-01 2.381520e-01 2.560019e-01 2.916384e-01
## theta[604] 2.268431e-01 2.489241e-01 2.742268e-01 3.274157e-01
## theta[605] 1.381210e-01 1.597596e-01 1.818215e-01 2.313135e-01
## theta[606] 2.295801e-01 2.530306e-01 2.756183e-01 3.186564e-01
## theta[607] 9.182783e-02 1.183956e-01 1.498973e-01 2.295350e-01
## theta[608] 1.328702e-01 1.532538e-01 1.776729e-01 2.264742e-01
## theta[609] 2.666161e-01 2.822876e-01 2.980031e-01 3.253154e-01
## theta[610] 2.157015e-01 2.380546e-01 2.615918e-01 3.048114e-01
## theta[611] 2.158424e-01 2.359211e-01 2.567191e-01 2.985726e-01
## theta[612] 2.498616e-01 2.701381e-01 2.932912e-01 3.380585e-01
## theta[613] 2.021545e-01 2.183387e-01 2.340682e-01 2.645383e-01
## theta[614] 8.133793e-02 1.030502e-01 1.284776e-01 1.809675e-01
## theta[615] 2.211792e-01 2.431521e-01 2.648207e-01 3.067722e-01
## theta[616] 9.041722e-02 1.165419e-01 1.458994e-01 2.118421e-01
## theta[617] 1.478979e-01 1.786314e-01 2.104563e-01 2.839007e-01
## theta[618] 2.785692e-01 2.890132e-01 2.994016e-01 3.229946e-01
## theta[619] 2.804558e-01 2.941688e-01 3.078316e-01 3.346309e-01
## theta[620] 2.231273e-01 2.461962e-01 2.699888e-01 3.159872e-01
## theta[621] 2.136586e-01 2.350912e-01 2.555073e-01 3.046246e-01
## theta[622] 8.808819e-02 1.147948e-01 1.469893e-01 2.162809e-01
## theta[623] 1.825549e-01 2.012653e-01 2.221431e-01 2.644170e-01
## theta[624] 2.358922e-01 2.462439e-01 2.590385e-01 2.807835e-01
## theta[625] 2.306524e-01 2.431735e-01 2.573459e-01 2.854237e-01
## theta[626] 2.418145e-01 2.628155e-01 2.853687e-01 3.301795e-01
## theta[627] 9.168885e-02 1.210097e-01 1.525488e-01 2.288463e-01
## theta[628] 3.148309e-01 3.282485e-01 3.412313e-01 3.692476e-01
## theta[629] 2.293929e-01 2.585936e-01 2.897992e-01 3.577490e-01
## theta[630] 9.144268e-02 1.188675e-01 1.527284e-01 2.289744e-01
## theta[631] 2.599445e-01 2.717327e-01 2.839636e-01 3.043167e-01
## theta[632] 9.220773e-02 1.197325e-01 1.523786e-01 2.266680e-01
## theta[633] 2.703824e-01 2.829445e-01 2.953118e-01 3.174054e-01
## theta[634] 2.473264e-01 2.594722e-01 2.735188e-01 2.990040e-01
## theta[635] 1.897303e-01 2.075655e-01 2.251635e-01 2.662770e-01
## theta[636] 2.187392e-01 2.336375e-01 2.505147e-01 2.850730e-01
## theta[637] 2.361497e-01 2.479504e-01 2.596905e-01 2.869079e-01
## theta[638] 2.615294e-01 2.721363e-01 2.835385e-01 3.064176e-01
## theta[639] 8.502238e-02 1.104236e-01 1.410272e-01 2.172558e-01
## theta[640] 3.076048e-01 3.197763e-01 3.318944e-01 3.555077e-01
## theta[641] 1.979344e-01 2.146626e-01 2.324074e-01 2.683670e-01
## theta[642] 2.655547e-01 2.772738e-01 2.893412e-01 3.155433e-01
## theta[643] 2.119961e-01 2.257885e-01 2.389709e-01 2.694706e-01
## theta[644] 2.382589e-01 2.500969e-01 2.619860e-01 2.849763e-01
## theta[645] 2.404986e-01 2.591179e-01 2.787198e-01 3.169583e-01
## theta[646] 2.096804e-01 2.274123e-01 2.454228e-01 2.759786e-01
## theta[647] 1.949570e-01 2.190441e-01 2.459788e-01 3.012546e-01
## theta[648] 9.405196e-02 1.247158e-01 1.609774e-01 2.369544e-01
## theta[649] 8.960240e-02 1.112542e-01 1.364603e-01 1.887583e-01
## theta[650] 2.451491e-01 2.669312e-01 2.882474e-01 3.325092e-01
## theta[651] 1.895658e-01 2.153064e-01 2.448847e-01 3.023763e-01
## theta[652] 9.029758e-02 1.185471e-01 1.509086e-01 2.308068e-01
## theta[653] 1.991302e-01 2.224765e-01 2.473517e-01 2.936476e-01
## theta[654] 7.892774e-02 9.909344e-02 1.183816e-01 1.646324e-01
## theta[655] 2.694019e-01 2.824837e-01 2.957128e-01 3.220781e-01
## theta[656] 2.329868e-01 2.433272e-01 2.552378e-01 2.755976e-01
## theta[657] 2.162359e-01 2.289010e-01 2.433369e-01 2.702649e-01
## theta[658] 1.842343e-01 2.027716e-01 2.219354e-01 2.610306e-01
## theta[659] 2.015534e-01 2.260747e-01 2.504931e-01 2.996305e-01
## theta[660] 1.023606e-01 1.279854e-01 1.601475e-01 2.285485e-01
## theta[661] 3.037696e-01 3.160163e-01 3.298437e-01 3.557959e-01
## theta[662] 8.920025e-02 1.163599e-01 1.517759e-01 2.218795e-01
## theta[663] 2.011555e-01 2.229914e-01 2.446494e-01 2.906308e-01
## theta[664] 2.551001e-01 2.697430e-01 2.841005e-01 3.124660e-01
## theta[665] 2.201105e-01 2.392232e-01 2.567192e-01 2.961835e-01
## theta[666] 1.958289e-01 2.146851e-01 2.355188e-01 2.789855e-01
## theta[667] 2.272537e-01 2.415825e-01 2.571892e-01 2.885022e-01
## theta[668] 2.415976e-01 2.575858e-01 2.732613e-01 3.080162e-01
## theta[669] 2.074923e-01 2.341975e-01 2.626243e-01 3.257053e-01
## theta[670] 9.404398e-02 1.242738e-01 1.568765e-01 2.234548e-01
## theta[671] 9.175289e-02 1.136611e-01 1.387768e-01 1.943481e-01
## theta[672] 9.418113e-02 1.219241e-01 1.517939e-01 2.190075e-01
## theta[673] 2.610092e-01 2.735095e-01 2.872825e-01 3.117676e-01
## theta[674] 9.417775e-02 1.217381e-01 1.535221e-01 2.266298e-01
## theta[675] 2.113776e-01 2.362654e-01 2.617312e-01 3.175237e-01
## theta[676] 1.653950e-01 1.816296e-01 1.960823e-01 2.291878e-01
## theta[677] 2.110338e-01 2.318394e-01 2.526120e-01 2.983438e-01
## theta[678] 2.777729e-01 2.896213e-01 3.027200e-01 3.284499e-01
## theta[679] 2.147113e-01 2.315700e-01 2.489706e-01 2.846878e-01
## theta[680] 2.566296e-01 2.689663e-01 2.806435e-01 3.055988e-01
## theta[681] 9.298193e-02 1.219687e-01 1.507978e-01 2.289911e-01
## theta[682] 2.507440e-01 2.721716e-01 2.952154e-01 3.428458e-01
## theta[683] 2.284707e-01 2.415848e-01 2.560082e-01 2.827563e-01
## theta[684] 2.588198e-01 2.702324e-01 2.821163e-01 3.076244e-01
## theta[685] 2.277200e-01 2.454129e-01 2.643796e-01 3.003670e-01
## theta[686] 2.209655e-01 2.385004e-01 2.584618e-01 2.962221e-01
## theta[687] 2.013211e-01 2.276975e-01 2.566860e-01 3.173375e-01
## theta[688] 2.018041e-01 2.164113e-01 2.318268e-01 2.598498e-01
## theta[689] 2.646984e-01 2.795189e-01 2.939236e-01 3.231262e-01
## theta[690] 9.760884e-02 1.200313e-01 1.427362e-01 1.934552e-01
## theta[691] 2.678659e-01 2.802331e-01 2.934663e-01 3.153457e-01
## theta[692] 1.888675e-01 2.060329e-01 2.232058e-01 2.584191e-01
## theta[693] 2.778140e-01 2.906387e-01 3.015362e-01 3.252943e-01
## theta[694] 7.649259e-02 9.331990e-02 1.115670e-01 1.549538e-01
## theta[695] 2.345488e-01 2.463257e-01 2.587699e-01 2.807678e-01
## theta[696] 2.656993e-01 2.808395e-01 2.967347e-01 3.260266e-01
## theta[697] 2.103745e-01 2.289140e-01 2.473720e-01 2.848254e-01
## theta[698] 2.626103e-01 2.851510e-01 3.097610e-01 3.593559e-01
## theta[699] 2.458552e-01 2.702880e-01 2.951155e-01 3.446967e-01
## theta[700] 2.139031e-01 2.310190e-01 2.485331e-01 2.857708e-01
## theta[701] 9.257602e-02 1.212230e-01 1.545043e-01 2.332693e-01
## theta[702] 1.026952e-01 1.302199e-01 1.645622e-01 2.357686e-01
## theta[703] 2.426881e-01 2.565819e-01 2.713746e-01 3.007568e-01
## theta[704] 2.926184e-01 3.055691e-01 3.179702e-01 3.421240e-01
## theta[705] 2.395457e-01 2.541008e-01 2.689773e-01 3.007952e-01
## theta[706] 2.496008e-01 2.611330e-01 2.735624e-01 2.999849e-01
## theta[707] 2.325528e-01 2.606686e-01 2.929737e-01 3.612096e-01
## theta[708] 2.425692e-01 2.551467e-01 2.677519e-01 2.954426e-01
## theta[709] 2.164809e-01 2.479364e-01 2.782418e-01 3.455342e-01
## theta[710] 2.042333e-01 2.189043e-01 2.345875e-01 2.675498e-01
## theta[711] 1.364718e-01 1.620105e-01 1.911378e-01 2.532467e-01
## theta[712] 1.059288e-01 1.337327e-01 1.669238e-01 2.355279e-01
## theta[713] 1.122760e-01 1.358514e-01 1.619373e-01 2.148836e-01
## theta[714] 2.289493e-01 2.422498e-01 2.548619e-01 2.801551e-01
## theta[715] 2.188394e-01 2.466600e-01 2.726872e-01 3.252064e-01
## theta[716] 2.616456e-01 2.770049e-01 2.930388e-01 3.239223e-01
## theta[717] 1.908872e-01 2.174598e-01 2.429718e-01 3.032748e-01
## theta[718] 9.331887e-02 1.201245e-01 1.529659e-01 2.161335e-01
## theta[719] 9.414573e-02 1.225871e-01 1.569177e-01 2.303111e-01
## theta[720] 2.220424e-01 2.383080e-01 2.565707e-01 2.919120e-01
## theta[721] 8.962236e-02 1.173695e-01 1.511777e-01 2.266142e-01
## theta[722] 2.223363e-01 2.328656e-01 2.425942e-01 2.634768e-01
## theta[723] 1.230568e-01 1.445316e-01 1.673501e-01 2.186030e-01
## theta[724] 1.057696e-01 1.343471e-01 1.650835e-01 2.436296e-01
## theta[725] 2.410021e-01 2.631521e-01 2.863161e-01 3.288545e-01
## theta[726] 2.177387e-01 2.424442e-01 2.661278e-01 3.203789e-01
## theta[727] 9.476373e-02 1.238487e-01 1.556733e-01 2.266699e-01
## theta[728] 9.238320e-02 1.198409e-01 1.514231e-01 2.336489e-01
## theta[729] 2.065178e-01 2.186160e-01 2.305881e-01 2.569931e-01
## theta[730] 2.929879e-01 3.040947e-01 3.156541e-01 3.375560e-01
## theta[731] 1.998708e-01 2.128776e-01 2.267422e-01 2.539319e-01
## theta[732] 2.621682e-01 2.771834e-01 2.925896e-01 3.268165e-01
## theta[733] 9.458037e-02 1.244779e-01 1.576685e-01 2.308131e-01
## theta[734] 2.358272e-01 2.554608e-01 2.750859e-01 3.126213e-01
## theta[735] 2.222031e-01 2.470352e-01 2.716842e-01 3.231844e-01
## theta[736] 6.926664e-02 8.713327e-02 1.082302e-01 1.533249e-01
## theta[737] 8.702041e-02 1.100450e-01 1.396832e-01 2.017013e-01
## theta[738] 1.260038e-01 1.465148e-01 1.699508e-01 2.229958e-01
## theta[739] 2.695783e-01 2.822030e-01 2.953399e-01 3.197248e-01
## theta[740] 2.381006e-01 2.591140e-01 2.784886e-01 3.271446e-01
## theta[741] 2.042162e-01 2.152207e-01 2.267699e-01 2.494900e-01
## theta[742] 9.065367e-02 1.125016e-01 1.365402e-01 1.936880e-01
## theta[743] 2.567761e-01 2.689758e-01 2.806669e-01 3.065120e-01
## theta[744] 2.110285e-01 2.295084e-01 2.482451e-01 2.835660e-01
## theta[745] 2.524664e-01 2.659851e-01 2.808317e-01 3.119409e-01
## theta[746] 2.140036e-01 2.293136e-01 2.439453e-01 2.747088e-01
## theta[747] 2.249013e-01 2.449214e-01 2.650345e-01 3.039093e-01
## theta[748] 2.165196e-01 2.476605e-01 2.770987e-01 3.350915e-01
## theta[749] 1.696000e-01 1.873356e-01 2.049663e-01 2.382380e-01
## theta[750] 2.563436e-01 2.694163e-01 2.825750e-01 3.095529e-01
## theta[751] 9.308393e-02 1.219385e-01 1.553708e-01 2.352574e-01
## theta[752] 1.814303e-01 1.956973e-01 2.116965e-01 2.442484e-01
## theta[753] 2.253825e-01 2.366662e-01 2.494568e-01 2.748540e-01
## theta[754] 2.420482e-01 2.593705e-01 2.766080e-01 3.133691e-01
## theta[755] 2.500122e-01 2.642646e-01 2.779247e-01 3.060419e-01
## theta[756] 8.969265e-02 1.079279e-01 1.291325e-01 1.715885e-01
## theta[757] 9.676240e-02 1.236753e-01 1.554467e-01 2.274167e-01
## theta[758] 2.276900e-01 2.466918e-01 2.677563e-01 3.086135e-01
## theta[759] 2.664493e-01 2.786733e-01 2.906448e-01 3.122053e-01
## theta[760] 2.703162e-01 2.874462e-01 3.048991e-01 3.357545e-01
## theta[761] 2.342706e-01 2.528756e-01 2.759006e-01 3.198187e-01
## theta[762] 9.188354e-02 1.210192e-01 1.580578e-01 2.267078e-01
## theta[763] 2.211275e-01 2.470073e-01 2.718654e-01 3.324770e-01
## theta[764] 1.067798e-01 1.366298e-01 1.739082e-01 2.545820e-01
## theta[765] 1.906778e-01 2.116244e-01 2.313690e-01 2.730934e-01
## theta[766] 9.695284e-02 1.255084e-01 1.556307e-01 2.205070e-01
## theta[767] 1.024369e-01 1.322164e-01 1.650952e-01 2.398266e-01
## theta[768] 2.461836e-01 2.596693e-01 2.723869e-01 2.978700e-01
## theta[769] 9.240644e-02 1.224214e-01 1.537095e-01 2.332247e-01
## theta[770] 2.391602e-01 2.548065e-01 2.720511e-01 3.094504e-01
## theta[771] 2.637408e-01 2.807785e-01 2.981284e-01 3.351918e-01
## theta[772] 2.343867e-01 2.480114e-01 2.616909e-01 2.880770e-01
## theta[773] 2.038053e-01 2.263661e-01 2.509074e-01 2.959270e-01
## theta[774] 2.041080e-01 2.300450e-01 2.576868e-01 3.129709e-01
## theta[775] 2.091020e-01 2.227471e-01 2.359885e-01 2.631272e-01
## theta[776] 2.297075e-01 2.418347e-01 2.547960e-01 2.800673e-01
## theta[777] 9.482854e-02 1.244531e-01 1.558149e-01 2.321660e-01
## theta[778] 2.365914e-01 2.528770e-01 2.704215e-01 3.027308e-01
## theta[779] 2.436131e-01 2.547369e-01 2.665371e-01 2.898311e-01
## theta[780] 9.404237e-02 1.154916e-01 1.397429e-01 1.946959e-01
## theta[781] 1.227798e-01 1.564150e-01 1.914387e-01 2.737869e-01
## theta[782] 2.012418e-01 2.160324e-01 2.323919e-01 2.624652e-01
## theta[783] 2.525273e-01 2.681941e-01 2.830251e-01 3.151137e-01
## theta[784] 2.682006e-01 2.794399e-01 2.907474e-01 3.125975e-01
## theta[785] 2.343619e-01 2.521344e-01 2.713194e-01 3.074822e-01
## theta[786] 2.146879e-01 2.292233e-01 2.442386e-01 2.758813e-01
## theta[787] 1.170241e-01 1.444391e-01 1.780962e-01 2.486507e-01
## theta[788] 1.721367e-01 1.979871e-01 2.283139e-01 2.863333e-01
## theta[789] 1.592497e-01 1.857839e-01 2.136082e-01 2.715216e-01
## theta[790] 9.266718e-02 1.231355e-01 1.566377e-01 2.323129e-01
## theta[791] 1.950423e-01 2.118875e-01 2.288328e-01 2.623412e-01
## theta[792] 9.387845e-02 1.217513e-01 1.547400e-01 2.185756e-01
## theta[793] 2.243262e-01 2.429384e-01 2.614437e-01 2.985879e-01
## theta[794] 2.158718e-01 2.458566e-01 2.732106e-01 3.279393e-01
## theta[795] 2.057001e-01 2.320960e-01 2.606426e-01 3.280078e-01
## theta[796] 1.980588e-01 2.213949e-01 2.439901e-01 2.933404e-01
## theta[797] 1.960111e-01 2.154397e-01 2.354398e-01 2.777524e-01
## theta[798] 1.829516e-01 2.055055e-01 2.285086e-01 2.726264e-01
## theta[799] 8.770110e-02 1.103709e-01 1.381666e-01 1.994243e-01
## theta[800] 2.159572e-01 2.411159e-01 2.699185e-01 3.273360e-01
## theta[801] 2.158538e-01 2.431934e-01 2.680979e-01 3.168262e-01
## theta[802] 9.253531e-02 1.206249e-01 1.507999e-01 2.332932e-01
## theta[803] 2.133227e-01 2.422520e-01 2.721322e-01 3.308061e-01
## theta[804] 1.475359e-01 1.711074e-01 1.958887e-01 2.522180e-01
## theta[805] 8.796306e-02 1.075390e-01 1.268009e-01 1.783065e-01
## theta[806] 9.608017e-02 1.231262e-01 1.508686e-01 2.298698e-01
## theta[807] 2.551808e-01 2.682092e-01 2.826755e-01 3.072267e-01
## theta[808] 2.266770e-01 2.418954e-01 2.569611e-01 2.874031e-01
## theta[809] 9.754683e-02 1.250409e-01 1.576356e-01 2.370508e-01
## theta[810] 1.170104e-01 1.453931e-01 1.795173e-01 2.569628e-01
## theta[811] 9.491401e-02 1.233090e-01 1.563217e-01 2.300275e-01
## theta[812] 5.639870e-02 7.295822e-02 9.242234e-02 1.382683e-01
## theta[813] 9.623051e-02 1.245434e-01 1.572787e-01 2.334329e-01
## theta[814] 1.077557e-01 1.332417e-01 1.657796e-01 2.375386e-01
## theta[815] 2.290803e-01 2.505444e-01 2.764638e-01 3.231283e-01
## theta[816] 2.418799e-01 2.599797e-01 2.803041e-01 3.176706e-01
## theta[817] 9.119156e-02 1.205607e-01 1.523779e-01 2.287126e-01
## theta[818] 2.275093e-01 2.460406e-01 2.665634e-01 3.079255e-01
## theta[819] 9.273848e-02 1.214439e-01 1.546590e-01 2.333424e-01
## theta[820] 2.914733e-01 3.034047e-01 3.156713e-01 3.378697e-01
## theta[821] 9.379888e-02 1.185596e-01 1.484707e-01 2.211853e-01
## theta[822] 2.159194e-01 2.366386e-01 2.568683e-01 2.966653e-01
## theta[823] 2.357270e-01 2.547645e-01 2.732916e-01 3.095267e-01
## theta[824] 2.382332e-01 2.553917e-01 2.724084e-01 3.089837e-01
## theta[825] 1.328382e-01 1.568503e-01 1.814635e-01 2.365173e-01
## theta[826] 2.150230e-01 2.323669e-01 2.503972e-01 2.891806e-01
## theta[827] 8.624349e-02 1.154844e-01 1.476755e-01 2.180607e-01
## theta[828] 1.046681e-01 1.240192e-01 1.443852e-01 1.904902e-01
## theta[829] 2.255197e-01 2.377291e-01 2.511531e-01 2.773868e-01
## theta[830] 2.549709e-01 2.739865e-01 2.934240e-01 3.299612e-01
## theta[831] 1.935890e-01 2.187955e-01 2.428589e-01 2.954027e-01
## theta[832] 2.255975e-01 2.388508e-01 2.531101e-01 2.826003e-01
## theta[833] 1.261024e-01 1.527355e-01 1.828017e-01 2.608192e-01
## theta[834] 9.191308e-02 1.176023e-01 1.488110e-01 2.113124e-01
## theta[835] 2.698109e-01 2.833719e-01 2.969164e-01 3.223141e-01
## theta[836] 2.056474e-01 2.236924e-01 2.432778e-01 2.825374e-01
## theta[837] 2.158793e-01 2.485769e-01 2.770959e-01 3.466309e-01
## theta[838] 2.209170e-01 2.345365e-01 2.479947e-01 2.764550e-01
## theta[839] 2.412670e-01 2.568397e-01 2.749749e-01 3.132682e-01
## theta[840] 2.252138e-01 2.427563e-01 2.617234e-01 2.992311e-01
## theta[841] 8.197193e-02 1.076152e-01 1.365960e-01 2.091259e-01
## theta[842] 1.003978e-01 1.301461e-01 1.601235e-01 2.365109e-01
## theta[843] 9.368657e-02 1.193490e-01 1.528498e-01 2.263633e-01
## theta[844] 8.475189e-02 1.114085e-01 1.445472e-01 2.200270e-01
## theta[845] 8.860227e-02 1.101445e-01 1.349183e-01 1.904866e-01
## theta[846] 2.213264e-01 2.364506e-01 2.517110e-01 2.817014e-01
## theta[847] 9.749566e-02 1.239424e-01 1.547656e-01 2.314544e-01
## theta[848] 1.237254e-01 1.516900e-01 1.869148e-01 2.664276e-01
## theta[849] 1.898780e-01 2.106983e-01 2.327216e-01 2.727071e-01
## theta[850] 1.108452e-01 1.389886e-01 1.718395e-01 2.452827e-01
## theta[851] 9.060475e-02 1.174237e-01 1.460999e-01 2.101674e-01
## theta[852] 1.291619e-01 1.501295e-01 1.735057e-01 2.272730e-01
## theta[853] 7.654607e-02 9.189232e-02 1.095074e-01 1.529817e-01
## theta[854] 2.373041e-01 2.550407e-01 2.750188e-01 3.111381e-01
## theta[855] 8.942535e-02 1.192264e-01 1.512069e-01 2.232414e-01
## theta[856] 2.442386e-01 2.664792e-01 2.890048e-01 3.361309e-01
## theta[857] 2.493240e-01 2.642690e-01 2.791316e-01 3.087445e-01
## theta[858] 2.628136e-01 2.788357e-01 2.957404e-01 3.264109e-01
## theta[859] 2.185642e-01 2.363349e-01 2.554552e-01 2.961835e-01
## theta[860] 2.484870e-01 2.617174e-01 2.756937e-01 3.021049e-01
## theta[861] 2.760322e-01 2.914732e-01 3.060148e-01 3.371660e-01
## theta[862] 1.850422e-01 2.086106e-01 2.317700e-01 2.799928e-01
## theta[863] 2.467161e-01 2.599176e-01 2.730694e-01 3.004221e-01
## theta[864] 2.319580e-01 2.532093e-01 2.760852e-01 3.280669e-01
## theta[865] 2.002868e-01 2.180735e-01 2.346025e-01 2.681838e-01
## theta[866] 9.771417e-02 1.217303e-01 1.511224e-01 2.212599e-01
## theta[867] 2.145521e-01 2.343205e-01 2.542451e-01 2.974569e-01
## theta[868] 9.584381e-02 1.230242e-01 1.562244e-01 2.303475e-01
## theta[869] 1.931254e-01 2.100847e-01 2.264297e-01 2.641484e-01
## theta[870] 2.567689e-01 2.791244e-01 3.000462e-01 3.446168e-01
## theta[871] 2.910010e-01 3.036195e-01 3.162367e-01 3.382706e-01
## theta[872] 1.978415e-01 2.203990e-01 2.442183e-01 2.897125e-01
## theta[873] 2.077662e-01 2.285397e-01 2.497931e-01 2.899183e-01
## theta[874] 2.586861e-01 2.772818e-01 2.982581e-01 3.316588e-01
## theta[875] 2.703742e-01 2.834163e-01 2.972481e-01 3.203266e-01
## theta[876] 2.576449e-01 2.701593e-01 2.822862e-01 3.049651e-01
## theta[877] 2.132606e-01 2.296137e-01 2.462285e-01 2.809196e-01
## theta[878] 1.261569e-01 1.468762e-01 1.703670e-01 2.232039e-01
## theta[879] 1.065538e-01 1.376575e-01 1.693522e-01 2.392844e-01
## theta[880] 2.401666e-01 2.520832e-01 2.634002e-01 2.867061e-01
## theta[881] 2.189537e-01 2.350524e-01 2.529469e-01 2.850305e-01
## theta[882] 9.939061e-02 1.271213e-01 1.607094e-01 2.461736e-01
## theta[883] 9.747939e-02 1.231534e-01 1.536777e-01 2.301379e-01
## theta[884] 2.105874e-01 2.361066e-01 2.631056e-01 3.229933e-01
## theta[885] 2.349986e-01 2.459272e-01 2.566665e-01 2.791083e-01
## theta[886] 1.304857e-01 1.578113e-01 1.864945e-01 2.482860e-01
## gamma[1] -1.115926e+00 -1.091657e+00 -1.068611e+00 -1.020864e+00
## gamma[2] -1.120508e+00 -1.093437e+00 -1.068703e+00 -1.015198e+00
## gamma[3] -1.092917e+00 -1.069208e+00 -1.044855e+00 -1.003147e+00
## gamma[4] -1.192251e+00 -1.167923e+00 -1.143318e+00 -1.100840e+00
## gamma[5] -1.076646e+00 -1.049632e+00 -1.021736e+00 -9.735275e-01
## gamma[6] -1.126171e+00 -1.105667e+00 -1.085225e+00 -1.046869e+00
## gamma[7] -1.942760e+00 -1.903746e+00 -1.867475e+00 -1.797326e+00
## gamma[8] -1.080933e+00 -1.054280e+00 -1.029175e+00 -9.821403e-01
## gamma[9] -1.132209e+00 -1.101251e+00 -1.072604e+00 -1.018191e+00
## alpha_w 7.301211e-03 1.951334e-02 3.202545e-02 5.411114e-02
## alpha_h -2.069775e-02 -7.713935e-03 3.248868e-03 2.442991e-02
## kappa[1] 9.164863e+01 1.051198e+02 1.221333e+02 1.589004e+02
## kappa[2] 8.717297e+01 1.029017e+02 1.184015e+02 1.546922e+02
## kappa[3] 8.111483e+01 9.418817e+01 1.084000e+02 1.446617e+02
## kappa[4] 7.725453e+01 8.854295e+01 1.016808e+02 1.324207e+02
## kappa[5] 7.849410e+01 9.308377e+01 1.084208e+02 1.455306e+02
## kappa[6] 9.085003e+01 1.041139e+02 1.215764e+02 1.566329e+02
## kappa[7] 4.399437e+01 5.229127e+01 6.150389e+01 8.365751e+01
## kappa[8] 8.991501e+01 1.080813e+02 1.280248e+02 1.698195e+02
## kappa[9] 7.465750e+01 8.874540e+01 1.035769e+02 1.378433e+02
## lp__ -8.742903e+04 -8.740122e+04 -8.737709e+04 -8.733054e+04
## n_eff Rhat
## theta[1] 1500.0000 0.9986802
## theta[2] 1500.0000 0.9994386
## theta[3] 1500.0000 0.9990138
## theta[4] 1500.0000 0.9989657
## theta[5] 1500.0000 0.9997996
## theta[6] 1500.0000 0.9985990
## theta[7] 1500.0000 0.9982463
## theta[8] 1500.0000 0.9986989
## theta[9] 1500.0000 0.9981607
## theta[10] 1500.0000 0.9985600
## theta[11] 1500.0000 0.9982727
## theta[12] 1500.0000 0.9981697
## theta[13] 1500.0000 0.9995716
## theta[14] 1500.0000 0.9993613
## theta[15] 1500.0000 0.9997304
## theta[16] 1500.0000 0.9988452
## theta[17] 1500.0000 0.9987006
## theta[18] 1500.0000 0.9992833
## theta[19] 1500.0000 0.9989995
## theta[20] 1500.0000 0.9987183
## theta[21] 1500.0000 0.9992136
## theta[22] 1500.0000 0.9986046
## theta[23] 1500.0000 0.9991146
## theta[24] 1500.0000 0.9987156
## theta[25] 1500.0000 0.9984408
## theta[26] 1500.0000 0.9993288
## theta[27] 1500.0000 0.9983983
## theta[28] 1500.0000 0.9987136
## theta[29] 1500.0000 0.9989461
## theta[30] 1500.0000 0.9984073
## theta[31] 1500.0000 1.0002085
## theta[32] 1500.0000 0.9985241
## theta[33] 1500.0000 0.9991705
## theta[34] 1500.0000 0.9989124
## theta[35] 1500.0000 0.9991034
## theta[36] 1500.0000 0.9982586
## theta[37] 1500.0000 0.9982493
## theta[38] 1500.0000 0.9993333
## theta[39] 1500.0000 0.9985131
## theta[40] 1500.0000 0.9987203
## theta[41] 1500.0000 0.9989021
## theta[42] 1500.0000 0.9985644
## theta[43] 1500.0000 0.9989674
## theta[44] 1500.0000 0.9982307
## theta[45] 1500.0000 0.9985706
## theta[46] 1500.0000 0.9981437
## theta[47] 1500.0000 0.9988277
## theta[48] 1500.0000 0.9985773
## theta[49] 1500.0000 0.9981924
## theta[50] 1500.0000 0.9982585
## theta[51] 1500.0000 0.9982794
## theta[52] 1500.0000 0.9989195
## theta[53] 1500.0000 0.9983474
## theta[54] 1500.0000 0.9992998
## theta[55] 1500.0000 0.9983116
## theta[56] 1500.0000 0.9987105
## theta[57] 1500.0000 0.9992516
## theta[58] 1500.0000 0.9985292
## theta[59] 1500.0000 0.9992683
## theta[60] 1500.0000 0.9986929
## theta[61] 1500.0000 0.9988100
## theta[62] 1500.0000 0.9984935
## theta[63] 1500.0000 0.9988780
## theta[64] 1500.0000 0.9988350
## theta[65] 1500.0000 0.9994963
## theta[66] 1500.0000 0.9983253
## theta[67] 1500.0000 1.0001605
## theta[68] 1500.0000 0.9988063
## theta[69] 1500.0000 0.9998771
## theta[70] 1500.0000 0.9983789
## theta[71] 1500.0000 0.9985706
## theta[72] 1500.0000 0.9988108
## theta[73] 1500.0000 0.9981213
## theta[74] 1500.0000 0.9985229
## theta[75] 1500.0000 0.9986473
## theta[76] 1500.0000 0.9992687
## theta[77] 1500.0000 0.9999323
## theta[78] 1500.0000 0.9982936
## theta[79] 1500.0000 0.9996408
## theta[80] 1500.0000 0.9987015
## theta[81] 1500.0000 1.0000299
## theta[82] 1500.0000 0.9990607
## theta[83] 1500.0000 0.9984647
## theta[84] 1500.0000 0.9992165
## theta[85] 1500.0000 1.0001734
## theta[86] 1500.0000 0.9995513
## theta[87] 1500.0000 1.0007369
## theta[88] 1500.0000 0.9994912
## theta[89] 1500.0000 0.9984755
## theta[90] 1500.0000 0.9989550
## theta[91] 1500.0000 0.9985647
## theta[92] 1500.0000 1.0003672
## theta[93] 1500.0000 0.9999391
## theta[94] 1500.0000 0.9989611
## theta[95] 1500.0000 0.9988338
## theta[96] 1500.0000 1.0004610
## theta[97] 1500.0000 0.9991299
## theta[98] 1500.0000 0.9994225
## theta[99] 1500.0000 0.9983026
## theta[100] 1500.0000 0.9989737
## theta[101] 1500.0000 0.9983506
## theta[102] 1500.0000 0.9987535
## theta[103] 1500.0000 0.9985770
## theta[104] 1500.0000 0.9987663
## theta[105] 1500.0000 0.9989586
## theta[106] 1500.0000 0.9982736
## theta[107] 1500.0000 0.9996929
## theta[108] 1500.0000 0.9982873
## theta[109] 1500.0000 0.9993628
## theta[110] 1500.0000 0.9985995
## theta[111] 1500.0000 0.9983859
## theta[112] 1500.0000 0.9988397
## theta[113] 1500.0000 0.9993426
## theta[114] 1500.0000 0.9987763
## theta[115] 1500.0000 0.9991591
## theta[116] 1500.0000 0.9991791
## theta[117] 1500.0000 0.9989487
## theta[118] 1500.0000 0.9985163
## theta[119] 1500.0000 0.9988103
## theta[120] 1500.0000 0.9991186
## theta[121] 1500.0000 0.9990040
## theta[122] 1500.0000 0.9988080
## theta[123] 1500.0000 0.9984200
## theta[124] 1500.0000 0.9995468
## theta[125] 1500.0000 0.9983689
## theta[126] 1500.0000 0.9983313
## theta[127] 1500.0000 0.9988544
## theta[128] 1500.0000 0.9987402
## theta[129] 1500.0000 0.9997670
## theta[130] 1500.0000 0.9990754
## theta[131] 1500.0000 0.9981984
## theta[132] 1500.0000 0.9984794
## theta[133] 1500.0000 1.0003355
## theta[134] 1500.0000 0.9984758
## theta[135] 1500.0000 0.9990804
## theta[136] 1500.0000 0.9995166
## theta[137] 1500.0000 0.9995341
## theta[138] 1500.0000 0.9999499
## theta[139] 1500.0000 0.9987503
## theta[140] 1500.0000 0.9990955
## theta[141] 1500.0000 0.9999419
## theta[142] 1500.0000 0.9995853
## theta[143] 1500.0000 0.9996990
## theta[144] 1500.0000 0.9980152
## theta[145] 1500.0000 0.9986973
## theta[146] 1500.0000 0.9986913
## theta[147] 1500.0000 1.0002366
## theta[148] 1500.0000 0.9998872
## theta[149] 1500.0000 1.0004509
## theta[150] 1500.0000 0.9996053
## theta[151] 1500.0000 0.9999448
## theta[152] 1500.0000 1.0004161
## theta[153] 1500.0000 0.9996788
## theta[154] 1500.0000 0.9995922
## theta[155] 1500.0000 0.9995880
## theta[156] 1500.0000 0.9998740
## theta[157] 1500.0000 0.9985966
## theta[158] 1500.0000 0.9985621
## theta[159] 1500.0000 1.0000986
## theta[160] 1500.0000 0.9995563
## theta[161] 1500.0000 0.9987259
## theta[162] 1500.0000 0.9984910
## theta[163] 1500.0000 1.0003592
## theta[164] 1500.0000 0.9986360
## theta[165] 1500.0000 0.9987254
## theta[166] 1500.0000 0.9998304
## theta[167] 1500.0000 0.9985194
## theta[168] 1500.0000 0.9985841
## theta[169] 1500.0000 0.9988193
## theta[170] 1500.0000 0.9996355
## theta[171] 1500.0000 0.9987293
## theta[172] 1500.0000 0.9985454
## theta[173] 1500.0000 0.9983521
## theta[174] 1500.0000 0.9990453
## theta[175] 1500.0000 0.9994846
## theta[176] 1500.0000 0.9985993
## theta[177] 1500.0000 0.9988523
## theta[178] 1500.0000 0.9991195
## theta[179] 1500.0000 0.9988975
## theta[180] 1500.0000 0.9990261
## theta[181] 1500.0000 0.9987528
## theta[182] 1500.0000 0.9986124
## theta[183] 1500.0000 1.0004372
## theta[184] 1500.0000 0.9982998
## theta[185] 1500.0000 0.9984625
## theta[186] 1500.0000 0.9985813
## theta[187] 1500.0000 0.9992390
## theta[188] 1500.0000 0.9982756
## theta[189] 1500.0000 0.9996814
## theta[190] 1500.0000 0.9984022
## theta[191] 1500.0000 0.9990586
## theta[192] 1500.0000 0.9988870
## theta[193] 1500.0000 0.9986581
## theta[194] 1500.0000 0.9994332
## theta[195] 1500.0000 0.9996775
## theta[196] 1500.0000 0.9994200
## theta[197] 1500.0000 0.9992091
## theta[198] 1500.0000 0.9982096
## theta[199] 1500.0000 0.9993441
## theta[200] 1500.0000 1.0001830
## theta[201] 1500.0000 0.9994077
## theta[202] 1500.0000 0.9992558
## theta[203] 1500.0000 0.9988741
## theta[204] 1500.0000 0.9988658
## theta[205] 1500.0000 0.9991044
## theta[206] 1500.0000 0.9994965
## theta[207] 1500.0000 0.9982979
## theta[208] 1500.0000 0.9999624
## theta[209] 1500.0000 0.9988978
## theta[210] 1500.0000 0.9988459
## theta[211] 1500.0000 0.9980384
## theta[212] 1500.0000 0.9989230
## theta[213] 1500.0000 0.9994659
## theta[214] 1500.0000 0.9981976
## theta[215] 1500.0000 0.9995312
## theta[216] 1500.0000 1.0009165
## theta[217] 1500.0000 0.9987773
## theta[218] 1500.0000 0.9982927
## theta[219] 1500.0000 0.9982866
## theta[220] 1500.0000 0.9993977
## theta[221] 1500.0000 0.9986547
## theta[222] 1500.0000 0.9993998
## theta[223] 1500.0000 0.9986314
## theta[224] 1500.0000 0.9987997
## theta[225] 1500.0000 0.9984774
## theta[226] 1500.0000 0.9983182
## theta[227] 1500.0000 0.9990486
## theta[228] 1500.0000 0.9992479
## theta[229] 1500.0000 0.9989593
## theta[230] 1500.0000 0.9997274
## theta[231] 1500.0000 0.9986090
## theta[232] 1500.0000 0.9986670
## theta[233] 1500.0000 0.9994208
## theta[234] 1500.0000 0.9990583
## theta[235] 1500.0000 0.9997103
## theta[236] 1500.0000 0.9992114
## theta[237] 1500.0000 0.9992355
## theta[238] 1500.0000 0.9987868
## theta[239] 1500.0000 0.9995505
## theta[240] 1500.0000 0.9991567
## theta[241] 1500.0000 0.9995793
## theta[242] 1500.0000 0.9990087
## theta[243] 1500.0000 0.9983017
## theta[244] 1500.0000 0.9994823
## theta[245] 1500.0000 0.9991931
## theta[246] 1500.0000 0.9982063
## theta[247] 1500.0000 0.9986002
## theta[248] 1500.0000 0.9988807
## theta[249] 1500.0000 0.9985382
## theta[250] 1500.0000 0.9986425
## theta[251] 1500.0000 0.9982692
## theta[252] 1500.0000 0.9987861
## theta[253] 1500.0000 0.9988045
## theta[254] 1500.0000 0.9985104
## theta[255] 1500.0000 0.9987726
## theta[256] 1500.0000 0.9996509
## theta[257] 1500.0000 0.9988235
## theta[258] 1500.0000 0.9992825
## theta[259] 1500.0000 0.9988159
## theta[260] 1500.0000 0.9985794
## theta[261] 1500.0000 0.9998546
## theta[262] 1500.0000 0.9981604
## theta[263] 1500.0000 0.9991245
## theta[264] 1500.0000 0.9985132
## theta[265] 1500.0000 0.9989543
## theta[266] 1500.0000 0.9987378
## theta[267] 1500.0000 0.9989873
## theta[268] 1500.0000 0.9982473
## theta[269] 1500.0000 0.9997262
## theta[270] 1500.0000 0.9996309
## theta[271] 1500.0000 0.9989308
## theta[272] 1500.0000 0.9995343
## theta[273] 1500.0000 0.9988732
## theta[274] 1500.0000 0.9987413
## theta[275] 1500.0000 0.9993505
## theta[276] 1500.0000 0.9983090
## theta[277] 1500.0000 0.9990352
## theta[278] 1500.0000 0.9991200
## theta[279] 1500.0000 0.9990224
## theta[280] 1500.0000 0.9988485
## theta[281] 1500.0000 0.9989068
## theta[282] 1500.0000 1.0014060
## theta[283] 1500.0000 0.9980231
## theta[284] 1500.0000 0.9991160
## theta[285] 1500.0000 0.9983171
## theta[286] 1500.0000 0.9987063
## theta[287] 1500.0000 0.9980645
## theta[288] 1500.0000 0.9986296
## theta[289] 1500.0000 0.9990579
## theta[290] 1500.0000 0.9998080
## theta[291] 1500.0000 0.9986111
## theta[292] 1500.0000 0.9981707
## theta[293] 1500.0000 0.9988134
## theta[294] 1500.0000 0.9985174
## theta[295] 1500.0000 0.9996799
## theta[296] 1500.0000 0.9989998
## theta[297] 1500.0000 0.9988039
## theta[298] 1500.0000 0.9985825
## theta[299] 1500.0000 0.9996477
## theta[300] 1500.0000 0.9993590
## theta[301] 1500.0000 0.9981124
## theta[302] 1500.0000 0.9985719
## theta[303] 1500.0000 0.9999593
## theta[304] 1500.0000 0.9981504
## theta[305] 1500.0000 0.9989598
## theta[306] 1500.0000 0.9999508
## theta[307] 1500.0000 0.9996275
## theta[308] 1500.0000 1.0000973
## theta[309] 1500.0000 0.9983805
## theta[310] 1500.0000 0.9987498
## theta[311] 1500.0000 1.0002912
## theta[312] 1500.0000 0.9989508
## theta[313] 1500.0000 0.9985128
## theta[314] 1500.0000 1.0006813
## theta[315] 1500.0000 0.9990306
## theta[316] 1500.0000 0.9985769
## theta[317] 1500.0000 0.9981134
## theta[318] 1500.0000 0.9991626
## theta[319] 1500.0000 0.9986332
## theta[320] 1500.0000 0.9997951
## theta[321] 1500.0000 0.9986552
## theta[322] 1500.0000 0.9983977
## theta[323] 1500.0000 0.9992215
## theta[324] 1500.0000 0.9985505
## theta[325] 1500.0000 0.9987175
## theta[326] 1500.0000 1.0004568
## theta[327] 1500.0000 0.9984753
## theta[328] 1500.0000 0.9984919
## theta[329] 1500.0000 0.9990975
## theta[330] 1500.0000 0.9985785
## theta[331] 1500.0000 0.9982498
## theta[332] 1500.0000 0.9993377
## theta[333] 1500.0000 0.9999738
## theta[334] 1500.0000 1.0019509
## theta[335] 1500.0000 0.9986828
## theta[336] 1500.0000 0.9981201
## theta[337] 1500.0000 0.9981886
## theta[338] 1500.0000 0.9996110
## theta[339] 1500.0000 0.9991671
## theta[340] 1500.0000 0.9994589
## theta[341] 1500.0000 0.9982957
## theta[342] 1500.0000 0.9980965
## theta[343] 1500.0000 0.9981441
## theta[344] 1500.0000 0.9997093
## theta[345] 1500.0000 0.9996991
## theta[346] 1500.0000 0.9981520
## theta[347] 1500.0000 0.9989119
## theta[348] 1500.0000 1.0000196
## theta[349] 1500.0000 0.9982505
## theta[350] 1500.0000 0.9989996
## theta[351] 1500.0000 0.9984364
## theta[352] 1500.0000 0.9996541
## theta[353] 1500.0000 0.9985547
## theta[354] 1500.0000 0.9983321
## theta[355] 1500.0000 0.9994471
## theta[356] 1500.0000 0.9984258
## theta[357] 1500.0000 1.0002155
## theta[358] 1500.0000 0.9987760
## theta[359] 1500.0000 0.9994392
## theta[360] 1500.0000 0.9993737
## theta[361] 1500.0000 0.9986416
## theta[362] 1500.0000 0.9985584
## theta[363] 1500.0000 0.9985906
## theta[364] 1500.0000 0.9982559
## theta[365] 1500.0000 0.9999024
## theta[366] 1500.0000 0.9982093
## theta[367] 1500.0000 0.9988151
## theta[368] 1500.0000 0.9993371
## theta[369] 1500.0000 0.9996461
## theta[370] 1500.0000 0.9985393
## theta[371] 1500.0000 0.9989055
## theta[372] 1500.0000 0.9988670
## theta[373] 1500.0000 0.9983394
## theta[374] 1500.0000 0.9988792
## theta[375] 1500.0000 0.9991289
## theta[376] 1500.0000 0.9984247
## theta[377] 1500.0000 0.9984680
## theta[378] 1500.0000 0.9985394
## theta[379] 1500.0000 0.9988900
## theta[380] 1500.0000 0.9992170
## theta[381] 1500.0000 0.9986323
## theta[382] 1500.0000 0.9988705
## theta[383] 1500.0000 0.9987165
## theta[384] 1500.0000 0.9999033
## theta[385] 1500.0000 0.9994831
## theta[386] 1500.0000 0.9992783
## theta[387] 1500.0000 1.0004433
## theta[388] 1500.0000 0.9989996
## theta[389] 1500.0000 0.9986944
## theta[390] 1500.0000 0.9989193
## theta[391] 1500.0000 0.9986450
## theta[392] 1500.0000 0.9989668
## theta[393] 1500.0000 1.0005442
## theta[394] 1500.0000 0.9984687
## theta[395] 1500.0000 1.0002803
## theta[396] 1500.0000 0.9993887
## theta[397] 1500.0000 1.0001571
## theta[398] 1500.0000 0.9987126
## theta[399] 1500.0000 0.9985477
## theta[400] 1500.0000 0.9990007
## theta[401] 1500.0000 0.9989477
## theta[402] 1500.0000 0.9993172
## theta[403] 1500.0000 0.9983908
## theta[404] 1500.0000 0.9991826
## theta[405] 1500.0000 0.9982333
## theta[406] 1500.0000 0.9981797
## theta[407] 1500.0000 0.9999299
## theta[408] 1500.0000 0.9986752
## theta[409] 1500.0000 0.9998351
## theta[410] 1500.0000 0.9990519
## theta[411] 1500.0000 0.9993934
## theta[412] 1500.0000 0.9983595
## theta[413] 1500.0000 0.9992302
## theta[414] 1500.0000 0.9985350
## theta[415] 1500.0000 0.9988415
## theta[416] 1500.0000 0.9989205
## theta[417] 1500.0000 0.9983516
## theta[418] 1500.0000 0.9986791
## theta[419] 1500.0000 0.9989900
## theta[420] 1500.0000 0.9982214
## theta[421] 1500.0000 0.9995384
## theta[422] 1500.0000 0.9988573
## theta[423] 1500.0000 0.9983760
## theta[424] 1500.0000 0.9991848
## theta[425] 1500.0000 0.9980910
## theta[426] 1500.0000 0.9996311
## theta[427] 1500.0000 0.9990080
## theta[428] 1500.0000 0.9986352
## theta[429] 1500.0000 0.9980845
## theta[430] 1500.0000 1.0001590
## theta[431] 1500.0000 0.9993548
## theta[432] 1500.0000 0.9993295
## theta[433] 1500.0000 0.9983809
## theta[434] 1500.0000 0.9985859
## theta[435] 1500.0000 0.9987899
## theta[436] 1500.0000 0.9996270
## theta[437] 1500.0000 0.9984159
## theta[438] 1500.0000 0.9987884
## theta[439] 1500.0000 0.9996083
## theta[440] 1500.0000 0.9982667
## theta[441] 1500.0000 0.9996149
## theta[442] 1500.0000 0.9985905
## theta[443] 1500.0000 0.9992022
## theta[444] 1500.0000 0.9999439
## theta[445] 1500.0000 1.0007069
## theta[446] 1500.0000 0.9991010
## theta[447] 1500.0000 0.9988386
## theta[448] 1500.0000 0.9983148
## theta[449] 1500.0000 0.9991091
## theta[450] 1500.0000 0.9986383
## theta[451] 1500.0000 0.9996961
## theta[452] 1500.0000 0.9984866
## theta[453] 1500.0000 0.9996494
## theta[454] 1500.0000 0.9983761
## theta[455] 1500.0000 0.9984707
## theta[456] 1500.0000 0.9997681
## theta[457] 1500.0000 0.9986182
## theta[458] 1500.0000 0.9982637
## theta[459] 1500.0000 0.9983298
## theta[460] 1500.0000 0.9987614
## theta[461] 1500.0000 0.9992462
## theta[462] 1500.0000 0.9980821
## theta[463] 1500.0000 0.9986665
## theta[464] 1500.0000 0.9991871
## theta[465] 1500.0000 0.9982420
## theta[466] 1500.0000 0.9986448
## theta[467] 1500.0000 0.9995708
## theta[468] 1500.0000 0.9987959
## theta[469] 1500.0000 0.9994643
## theta[470] 1500.0000 0.9983947
## theta[471] 1500.0000 0.9983091
## theta[472] 1500.0000 0.9994247
## theta[473] 1500.0000 0.9989738
## theta[474] 1500.0000 0.9985204
## theta[475] 1500.0000 0.9998375
## theta[476] 1500.0000 1.0002757
## theta[477] 1500.0000 0.9985850
## theta[478] 1500.0000 0.9983190
## theta[479] 1500.0000 0.9992548
## theta[480] 1500.0000 0.9987266
## theta[481] 1500.0000 0.9989528
## theta[482] 1500.0000 0.9985390
## theta[483] 1500.0000 0.9988106
## theta[484] 1500.0000 1.0000338
## theta[485] 1500.0000 0.9983921
## theta[486] 1500.0000 0.9987305
## theta[487] 1500.0000 0.9992268
## theta[488] 1500.0000 0.9990249
## theta[489] 1500.0000 0.9991021
## theta[490] 1500.0000 0.9987208
## theta[491] 1500.0000 0.9993672
## theta[492] 1500.0000 0.9984762
## theta[493] 1500.0000 0.9984599
## theta[494] 1500.0000 0.9991646
## theta[495] 1500.0000 0.9992666
## theta[496] 1500.0000 0.9981933
## theta[497] 1500.0000 0.9982859
## theta[498] 1500.0000 0.9984555
## theta[499] 1500.0000 0.9994953
## theta[500] 1500.0000 0.9981621
## theta[501] 1500.0000 0.9988270
## theta[502] 1500.0000 0.9988350
## theta[503] 1500.0000 0.9991473
## theta[504] 1500.0000 0.9990995
## theta[505] 1500.0000 1.0006153
## theta[506] 1500.0000 0.9982826
## theta[507] 1500.0000 0.9991672
## theta[508] 1500.0000 0.9991178
## theta[509] 1500.0000 0.9987350
## theta[510] 1500.0000 0.9995700
## theta[511] 1500.0000 0.9985136
## theta[512] 1500.0000 0.9991317
## theta[513] 1500.0000 0.9992024
## theta[514] 1500.0000 0.9986525
## theta[515] 1500.0000 0.9987489
## theta[516] 1500.0000 0.9985548
## theta[517] 1500.0000 1.0000560
## theta[518] 1500.0000 0.9995085
## theta[519] 1500.0000 0.9986310
## theta[520] 1500.0000 0.9982802
## theta[521] 1500.0000 0.9981959
## theta[522] 1500.0000 1.0000722
## theta[523] 1500.0000 0.9984633
## theta[524] 1500.0000 1.0000377
## theta[525] 1500.0000 0.9996655
## theta[526] 1500.0000 0.9990246
## theta[527] 1500.0000 0.9994729
## theta[528] 1500.0000 0.9987297
## theta[529] 1500.0000 0.9991102
## theta[530] 1500.0000 0.9992416
## theta[531] 1500.0000 0.9987277
## theta[532] 1500.0000 0.9987474
## theta[533] 1500.0000 0.9987429
## theta[534] 1500.0000 1.0013383
## theta[535] 1500.0000 0.9990714
## theta[536] 1500.0000 0.9992006
## theta[537] 1500.0000 0.9987074
## theta[538] 1500.0000 0.9988644
## theta[539] 1500.0000 0.9989006
## theta[540] 1500.0000 0.9982642
## theta[541] 1500.0000 0.9987119
## theta[542] 1500.0000 0.9987771
## theta[543] 1500.0000 0.9980642
## theta[544] 1500.0000 0.9990203
## theta[545] 1500.0000 0.9992572
## theta[546] 1500.0000 0.9988531
## theta[547] 1500.0000 0.9989361
## theta[548] 1500.0000 1.0009326
## theta[549] 1500.0000 0.9985183
## theta[550] 1500.0000 0.9986608
## theta[551] 1500.0000 1.0002308
## theta[552] 1500.0000 0.9995074
## theta[553] 1500.0000 0.9984213
## theta[554] 1500.0000 0.9986443
## theta[555] 1500.0000 0.9989176
## theta[556] 1500.0000 0.9987609
## theta[557] 1500.0000 0.9985928
## theta[558] 1500.0000 1.0003455
## theta[559] 1500.0000 1.0003934
## theta[560] 1500.0000 0.9992190
## theta[561] 1500.0000 0.9992885
## theta[562] 1500.0000 0.9989473
## theta[563] 1500.0000 0.9989374
## theta[564] 1500.0000 0.9980815
## theta[565] 1500.0000 0.9987498
## theta[566] 1500.0000 0.9988859
## theta[567] 1500.0000 0.9989338
## theta[568] 1500.0000 0.9995765
## theta[569] 1500.0000 0.9992875
## theta[570] 1500.0000 0.9987448
## theta[571] 1500.0000 0.9988619
## theta[572] 1500.0000 0.9981030
## theta[573] 1500.0000 0.9991973
## theta[574] 1500.0000 0.9989603
## theta[575] 1500.0000 0.9989179
## theta[576] 1500.0000 0.9988051
## theta[577] 1500.0000 0.9985490
## theta[578] 1500.0000 0.9999552
## theta[579] 1500.0000 0.9985708
## theta[580] 1500.0000 1.0005815
## theta[581] 1500.0000 0.9987397
## theta[582] 1500.0000 0.9991065
## theta[583] 1500.0000 0.9983912
## theta[584] 1500.0000 0.9983308
## theta[585] 1500.0000 0.9987970
## theta[586] 1500.0000 0.9984487
## theta[587] 1500.0000 0.9996030
## theta[588] 1500.0000 1.0005831
## theta[589] 1500.0000 0.9988608
## theta[590] 1500.0000 0.9987212
## theta[591] 1500.0000 0.9988440
## theta[592] 1500.0000 0.9992372
## theta[593] 1500.0000 0.9985676
## theta[594] 1500.0000 0.9993781
## theta[595] 1500.0000 0.9995713
## theta[596] 1500.0000 0.9982206
## theta[597] 1500.0000 0.9986891
## theta[598] 1500.0000 0.9993135
## theta[599] 1500.0000 0.9981159
## theta[600] 1500.0000 1.0007273
## theta[601] 1500.0000 0.9986773
## theta[602] 1500.0000 0.9984922
## theta[603] 1500.0000 1.0001673
## theta[604] 1500.0000 0.9988773
## theta[605] 1500.0000 0.9991967
## theta[606] 1500.0000 0.9985453
## theta[607] 1500.0000 0.9990837
## theta[608] 1500.0000 0.9988243
## theta[609] 1500.0000 0.9986402
## theta[610] 1500.0000 0.9986940
## theta[611] 1500.0000 1.0000581
## theta[612] 1500.0000 0.9987352
## theta[613] 1500.0000 0.9987204
## theta[614] 1500.0000 1.0000133
## theta[615] 1500.0000 0.9997731
## theta[616] 1500.0000 0.9996309
## theta[617] 1500.0000 1.0001200
## theta[618] 1500.0000 1.0000898
## theta[619] 1500.0000 0.9985509
## theta[620] 1500.0000 0.9984885
## theta[621] 1500.0000 0.9988921
## theta[622] 1500.0000 0.9991853
## theta[623] 1500.0000 0.9984573
## theta[624] 1500.0000 0.9993631
## theta[625] 1500.0000 0.9986682
## theta[626] 1500.0000 0.9987341
## theta[627] 1500.0000 0.9986097
## theta[628] 1500.0000 0.9989013
## theta[629] 1500.0000 0.9988773
## theta[630] 1500.0000 0.9992965
## theta[631] 1500.0000 0.9987113
## theta[632] 1500.0000 1.0010117
## theta[633] 1500.0000 0.9986101
## theta[634] 1500.0000 0.9982685
## theta[635] 1500.0000 0.9985997
## theta[636] 1500.0000 0.9984787
## theta[637] 1500.0000 0.9997041
## theta[638] 1500.0000 0.9984284
## theta[639] 1500.0000 0.9985681
## theta[640] 1500.0000 0.9985290
## theta[641] 1500.0000 0.9990115
## theta[642] 1500.0000 0.9986471
## theta[643] 1500.0000 0.9997237
## theta[644] 1500.0000 0.9992678
## theta[645] 1500.0000 0.9993084
## theta[646] 1500.0000 0.9993065
## theta[647] 1500.0000 0.9989108
## theta[648] 1500.0000 0.9981570
## theta[649] 1500.0000 0.9986380
## theta[650] 1500.0000 0.9990163
## theta[651] 1500.0000 0.9987219
## theta[652] 1500.0000 0.9992157
## theta[653] 1500.0000 0.9991127
## theta[654] 1500.0000 0.9989317
## theta[655] 1500.0000 0.9987896
## theta[656] 1500.0000 0.9982579
## theta[657] 1500.0000 0.9995526
## theta[658] 1500.0000 0.9991206
## theta[659] 1500.0000 0.9982527
## theta[660] 1500.0000 0.9981646
## theta[661] 1500.0000 0.9985076
## theta[662] 1500.0000 0.9989453
## theta[663] 1500.0000 0.9993746
## theta[664] 1500.0000 0.9989623
## theta[665] 1500.0000 1.0005643
## theta[666] 1500.0000 0.9981290
## theta[667] 1500.0000 0.9982991
## theta[668] 1500.0000 0.9983455
## theta[669] 1500.0000 0.9990679
## theta[670] 1500.0000 0.9991621
## theta[671] 1500.0000 0.9998500
## theta[672] 1500.0000 0.9987746
## theta[673] 1500.0000 0.9986855
## theta[674] 1500.0000 0.9988541
## theta[675] 1500.0000 0.9992257
## theta[676] 1500.0000 0.9985197
## theta[677] 1500.0000 1.0007344
## theta[678] 1500.0000 0.9996461
## theta[679] 1500.0000 1.0000276
## theta[680] 1500.0000 0.9989094
## theta[681] 1500.0000 0.9991898
## theta[682] 1500.0000 0.9985229
## theta[683] 1500.0000 0.9984635
## theta[684] 1500.0000 0.9990154
## theta[685] 1500.0000 0.9988957
## theta[686] 1500.0000 0.9984252
## theta[687] 1500.0000 0.9992140
## theta[688] 1500.0000 0.9996784
## theta[689] 1500.0000 0.9983276
## theta[690] 1500.0000 1.0002054
## theta[691] 1500.0000 0.9981645
## theta[692] 1500.0000 0.9993600
## theta[693] 1500.0000 1.0004823
## theta[694] 1500.0000 0.9997683
## theta[695] 1500.0000 0.9988499
## theta[696] 1500.0000 0.9998452
## theta[697] 1500.0000 0.9987501
## theta[698] 1500.0000 0.9985736
## theta[699] 1500.0000 0.9993992
## theta[700] 1500.0000 0.9985275
## theta[701] 1500.0000 0.9993313
## theta[702] 1500.0000 0.9987847
## theta[703] 1500.0000 0.9992057
## theta[704] 1500.0000 0.9989164
## theta[705] 1500.0000 0.9998076
## theta[706] 1500.0000 0.9994214
## theta[707] 1500.0000 0.9988706
## theta[708] 1500.0000 0.9996704
## theta[709] 1500.0000 0.9991728
## theta[710] 1500.0000 0.9987155
## theta[711] 1500.0000 0.9990246
## theta[712] 1500.0000 0.9987008
## theta[713] 1500.0000 0.9998609
## theta[714] 1500.0000 0.9985012
## theta[715] 1500.0000 0.9989462
## theta[716] 1500.0000 0.9990844
## theta[717] 1500.0000 0.9988211
## theta[718] 1500.0000 0.9987268
## theta[719] 1500.0000 0.9987646
## theta[720] 1500.0000 0.9990589
## theta[721] 1500.0000 0.9986478
## theta[722] 1500.0000 0.9983682
## theta[723] 1500.0000 0.9991634
## theta[724] 1500.0000 0.9983136
## theta[725] 1500.0000 0.9986238
## theta[726] 1500.0000 0.9988512
## theta[727] 1500.0000 0.9982728
## theta[728] 1500.0000 0.9988857
## theta[729] 1500.0000 0.9986511
## theta[730] 1500.0000 0.9984996
## theta[731] 1500.0000 0.9991041
## theta[732] 1500.0000 0.9989428
## theta[733] 1500.0000 0.9989207
## theta[734] 1500.0000 0.9983986
## theta[735] 1500.0000 0.9988567
## theta[736] 1500.0000 0.9985713
## theta[737] 1500.0000 0.9992938
## theta[738] 1500.0000 0.9988691
## theta[739] 1500.0000 0.9988876
## theta[740] 1500.0000 0.9981659
## theta[741] 1500.0000 1.0011589
## theta[742] 1500.0000 0.9982790
## theta[743] 1500.0000 1.0008122
## theta[744] 1500.0000 0.9987366
## theta[745] 1500.0000 0.9981805
## theta[746] 1500.0000 0.9991822
## theta[747] 1500.0000 1.0003639
## theta[748] 1500.0000 0.9985017
## theta[749] 1500.0000 0.9989997
## theta[750] 1500.0000 0.9983869
## theta[751] 1500.0000 1.0006513
## theta[752] 1500.0000 0.9988907
## theta[753] 1500.0000 0.9980753
## theta[754] 1500.0000 0.9989843
## theta[755] 1500.0000 0.9983738
## theta[756] 1500.0000 0.9985216
## theta[757] 1500.0000 0.9986068
## theta[758] 1500.0000 0.9984038
## theta[759] 1500.0000 0.9985685
## theta[760] 1500.0000 0.9998379
## theta[761] 1500.0000 0.9982914
## theta[762] 1500.0000 0.9983112
## theta[763] 1500.0000 0.9985249
## theta[764] 1500.0000 1.0000425
## theta[765] 1500.0000 0.9986797
## theta[766] 1500.0000 0.9989628
## theta[767] 1500.0000 0.9983276
## theta[768] 1500.0000 0.9992874
## theta[769] 1500.0000 0.9987581
## theta[770] 1500.0000 0.9983046
## theta[771] 1500.0000 0.9984530
## theta[772] 1500.0000 0.9995334
## theta[773] 1500.0000 0.9990758
## theta[774] 1500.0000 0.9992583
## theta[775] 1500.0000 0.9988212
## theta[776] 1500.0000 0.9986868
## theta[777] 1500.0000 0.9982581
## theta[778] 1500.0000 0.9984107
## theta[779] 1500.0000 0.9988389
## theta[780] 1500.0000 0.9986854
## theta[781] 1500.0000 0.9992168
## theta[782] 1500.0000 0.9985537
## theta[783] 1500.0000 0.9983511
## theta[784] 1500.0000 0.9987850
## theta[785] 1500.0000 0.9982842
## theta[786] 1500.0000 0.9986129
## theta[787] 1500.0000 0.9995177
## theta[788] 1500.0000 1.0000572
## theta[789] 1500.0000 0.9993895
## theta[790] 1500.0000 0.9998470
## theta[791] 1500.0000 1.0001946
## theta[792] 1500.0000 0.9999385
## theta[793] 1500.0000 0.9994553
## theta[794] 1500.0000 0.9994788
## theta[795] 1500.0000 0.9987990
## theta[796] 1500.0000 0.9984770
## theta[797] 1500.0000 0.9983640
## theta[798] 1500.0000 0.9982776
## theta[799] 1500.0000 1.0003473
## theta[800] 1500.0000 0.9990969
## theta[801] 1500.0000 0.9990397
## theta[802] 1500.0000 0.9982617
## theta[803] 1500.0000 0.9981585
## theta[804] 1500.0000 0.9996143
## theta[805] 1500.0000 0.9988699
## theta[806] 1500.0000 0.9987137
## theta[807] 1500.0000 0.9985740
## theta[808] 1500.0000 0.9997871
## theta[809] 1500.0000 0.9980981
## theta[810] 1500.0000 0.9987673
## theta[811] 1500.0000 0.9983301
## theta[812] 1500.0000 0.9988867
## theta[813] 1500.0000 0.9987494
## theta[814] 1500.0000 0.9992346
## theta[815] 1500.0000 0.9985025
## theta[816] 1500.0000 0.9989512
## theta[817] 1500.0000 0.9981953
## theta[818] 1500.0000 0.9990877
## theta[819] 1500.0000 0.9993107
## theta[820] 1500.0000 0.9986131
## theta[821] 1500.0000 0.9989478
## theta[822] 1500.0000 0.9993212
## theta[823] 1500.0000 1.0006105
## theta[824] 1500.0000 0.9986526
## theta[825] 1500.0000 0.9996001
## theta[826] 1500.0000 0.9988365
## theta[827] 1500.0000 0.9989965
## theta[828] 1500.0000 0.9986741
## theta[829] 1500.0000 0.9989078
## theta[830] 1500.0000 0.9991468
## theta[831] 1500.0000 0.9996310
## theta[832] 1500.0000 0.9984335
## theta[833] 1500.0000 0.9986053
## theta[834] 1500.0000 0.9983446
## theta[835] 1500.0000 0.9987817
## theta[836] 1500.0000 0.9986567
## theta[837] 1500.0000 0.9995807
## theta[838] 1500.0000 0.9992002
## theta[839] 1500.0000 0.9986086
## theta[840] 1500.0000 0.9985745
## theta[841] 1500.0000 0.9987720
## theta[842] 1500.0000 0.9984692
## theta[843] 1500.0000 1.0003919
## theta[844] 1500.0000 0.9985214
## theta[845] 1500.0000 0.9992376
## theta[846] 1500.0000 0.9983309
## theta[847] 1500.0000 0.9991389
## theta[848] 1500.0000 0.9993915
## theta[849] 1500.0000 0.9988228
## theta[850] 1500.0000 0.9986631
## theta[851] 1500.0000 0.9987907
## theta[852] 1500.0000 0.9985084
## theta[853] 1500.0000 0.9995035
## theta[854] 1500.0000 0.9987358
## theta[855] 1500.0000 0.9983504
## theta[856] 1500.0000 0.9992454
## theta[857] 1500.0000 0.9989834
## theta[858] 1500.0000 0.9986032
## theta[859] 1500.0000 0.9998188
## theta[860] 1500.0000 0.9989876
## theta[861] 1500.0000 0.9987638
## theta[862] 1500.0000 0.9981627
## theta[863] 1500.0000 0.9985091
## theta[864] 1500.0000 0.9993502
## theta[865] 1500.0000 0.9996747
## theta[866] 1500.0000 0.9992696
## theta[867] 1500.0000 0.9993032
## theta[868] 1500.0000 0.9996104
## theta[869] 1500.0000 0.9986633
## theta[870] 1500.0000 0.9982331
## theta[871] 1500.0000 0.9982869
## theta[872] 1500.0000 0.9983833
## theta[873] 1500.0000 0.9984807
## theta[874] 1500.0000 0.9981381
## theta[875] 1500.0000 0.9982900
## theta[876] 1500.0000 0.9990818
## theta[877] 1500.0000 0.9988614
## theta[878] 1500.0000 0.9989267
## theta[879] 1500.0000 0.9983237
## theta[880] 1500.0000 0.9990078
## theta[881] 1500.0000 0.9990675
## theta[882] 1500.0000 0.9983744
## theta[883] 1500.0000 0.9991576
## theta[884] 1500.0000 1.0000931
## theta[885] 1500.0000 0.9983194
## theta[886] 1500.0000 0.9996269
## gamma[1] 1500.0000 0.9997262
## gamma[2] 1500.0000 1.0017117
## gamma[3] 1500.0000 0.9993687
## gamma[4] 1500.0000 1.0002380
## gamma[5] 1500.0000 0.9988730
## gamma[6] 1500.0000 0.9989104
## gamma[7] 615.5653 1.0016183
## gamma[8] 1500.0000 1.0002329
## gamma[9] 1500.0000 0.9995473
## alpha_w 1500.0000 1.0065264
## alpha_h 1500.0000 1.0021712
## kappa[1] 995.4217 0.9995813
## kappa[2] 1500.0000 1.0003780
## kappa[3] 1500.0000 0.9997823
## kappa[4] 1029.5624 1.0002799
## kappa[5] 1500.0000 1.0004720
## kappa[6] 802.4592 0.9995102
## kappa[7] 128.0893 1.0214134
## kappa[8] 1500.0000 0.9989129
## kappa[9] 1500.0000 1.0005137
## lp__ 137.5094 1.0126180Pitchers still don’t bat well
## ci_level: 0.8 (80% intervals)## outer_level: 0.95 (95% intervals)
Recall the mean of \(\theta_i\) is \[\begin{aligned} \mu_i = \frac{1}{1 + \exp(-\gamma_{p_i} - \alpha_h h_i - \alpha_w w_i)} . \end{aligned}\]
gamma_samples <- rstan::extract(logistic_fit)$gamma
colnames(gamma_samples) <- levels(batplus$PriPos)
mu_samples <- 1/(1+exp(-gamma_samples))
boxplot(mu_samples, ylab="posterior distrn, mean batting avg", las=3)
No effect of height or weight
## ci_level: 0.8 (80% intervals)## outer_level: 0.95 (95% intervals)
Same \(\theta\) as before?
new_post_theta <- colMeans(rstan::extract(logistic_fit)$theta)
old_post_theta <- batting$post_mean[match(batplus$Player, batting$Player)]
plot(old_post_theta, new_post_theta, xlab="theta, model 1", ylab="theta, model 2")
abline(0,1, col='red')
Conclusions
We don’t have good evidence that batting average varies substantially with height or weight.
Changing the model from a Beta prior on class means to a logistic transform of a linear model did not substantially affect the results.
Stochastic minute
If \(X \sim \Cauchy(\text{center}=\mu, \text{scale}=\sigma)\), then \(X\) has probability density \[\begin{aligned} f(x \given \mu, \sigma) = \frac{1}{\pi\left( 1 + \left( \frac{x - \mu}{\sigma} \right)^2 \right)} . \end{aligned}\]
The Cauchy is a good example of a distribution with “heavy tails”: rare, very large values.
If \(Z \sim \Normal(0, 1)\) and \(X ~ \Normal(0,1/Z)\) then \(X \sim \Cauchy(0,1)\).
If \(X_1, X_2, \ldots, X_n\) are independent \(\Cauchy(0,1)\) then \(\max(X_1, \ldots, X_n)\) is of size \(n\).
If \(X_1, X_2, \ldots, X_n\) are independent \(\Cauchy(0,1)\) then \[\begin{aligned} \frac{1}{n} \left(X_1 + \cdots + X_n\right) \sim \Cauchy(0,1) . \end{aligned}\]
- If \(X_1, X_2, \ldots, X_n\) are independent \(\Cauchy(0,1)\) then \[\begin{aligned} \frac{1}{n} \left(X_1 + \cdots + X_n\right) \sim \Cauchy(0,1) . \end{aligned}\]
Wait, what?!?
A single value has the same distribution as the mean of 1,000 of them?
Let’s look:
\(X \sim \Normal(0,1)\)
\(X \sim \Cauchy(0,1)\)
Another way to look at it: extreme values
n <- 100
plot(c(cummax(rcauchy(n))), type='l', ylab='max value so far', xlab='number of samples', col='red')
lines(c(cummax(rnorm(n))), col='black')
legend("bottomright", lty=1, col=c('black', 'red'), legend=c('normal', 'cauchy'))
Another way to look at it: extreme values
n <- 1000
plot(c(cummax(rcauchy(n))), type='l', ylab='max value so far', xlab='number of samples', col='red')
lines(c(cummax(rnorm(n))), col='black')
legend("bottomright", lty=1, col=c('black', 'red'), legend=c('normal', 'cauchy'))
Another way to look at it: extreme values
n <- 1e6
plot(c(cummax(rcauchy(n))), type='l', ylab='max value so far', xlab='number of samples', col='red')
lines(c(cummax(rnorm(n))), col='black')
legend("bottomright", lty=1, col=c('black', 'red'), legend=c('normal', 'cauchy'))
Exercise: mixture of error rates.
Suppose you are measuring relative metabolic rates of mice in the wild. Because life is complicated, the accuracy of your measurements varies widely. A model of the measured rate, \(R_i\), for a mouse at temperature \(T_i\) is \[\begin{aligned} R &\sim \Normal(120 + 0.7 * (T_i - 37), 1/E) \\ E &\sim \Normal(0, 1) . \end{aligned}\]
Simulate 200 measurements from this model, for temperatures between 36 and 38, and try to infer the true slope (0.7).
Robust regression
Standard linear regression
\[\begin{aligned} \hat y_i &= b_0 + b_1 x_i \\ y_i &\sim \Normal(\hat y_i, \sigma^2) . \end{aligned}\]
Simulate data:
Standard linear regression
## user system elapsed
## 0.004 0.000 0.004##
## Call:
## lm(formula = y ~ x)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.50761 -0.35521 -0.00729 0.29981 1.35287
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.97426 0.03689 26.41 <2e-16 ***
## x 2.02372 0.03610 56.05 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5188 on 198 degrees of freedom
## Multiple R-squared: 0.9407, Adjusted R-squared: 0.9404
## F-statistic: 3142 on 1 and 198 DF, p-value: < 2.2e-16with Stan
slr_block <- "
data {
int N;
vector[N] x;
vector[N] y;
}
parameters {
real b0;
real b1;
real<lower=0> sigma;
}
model {
y ~ normal(b0 + b1*x, sigma);
}"
system.time(
stanlr <- stan(model_code=slr_block,
data=list(N=length(x), x=x, y=y), iter=1e3))## user system elapsed
## 43.510 1.090 46.522## Inference for Stan model: 3b05fdd2691a18718e9286fd7f1e1ac1.
## 4 chains, each with iter=1000; warmup=500; thin=1;
## post-warmup draws per chain=500, total post-warmup draws=2000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## b0 0.97 0.00 0.04 0.90 0.95 0.97 1.00 1.05 1723 1.00
## b1 2.02 0.00 0.04 1.95 2.00 2.02 2.05 2.10 2000 1.00
## sigma 0.52 0.00 0.03 0.48 0.50 0.52 0.54 0.57 2000 1.00
## lp__ 30.06 0.04 1.25 26.93 29.52 30.39 30.96 31.46 847 1.01
##
## Samples were drawn using NUTS(diag_e) at Wed Nov 28 21:28:58 2018.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).Cauchy noise?
Relative axon growth for neurons after \(x\) hours:
Standard linear regression
## user system elapsed
## 0.001 0.000 0.002##
## Call:
## lm(formula = y ~ x)
##
## Residuals:
## Min 1Q Median 3Q Max
## -65.973 -0.877 0.120 1.312 66.074
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.8918 0.5740 1.554 0.122
## x 0.7230 0.6172 1.171 0.243
##
## Residual standard error: 8.117 on 198 degrees of freedom
## Multiple R-squared: 0.006883, Adjusted R-squared: 0.001868
## F-statistic: 1.372 on 1 and 198 DF, p-value: 0.2428with Stan
srr_block <- "
data {
int N;
vector[N] x;
vector[N] y;
}
parameters {
real b0;
real b1;
real<lower=0> sigma;
}
model {
y ~ cauchy(b0 + b1*x, sigma);
}"
system.time(
stanrr <- stan(model_code=srr_block,
data=list(N=length(x), x=x, y=y), iter=1e3))## user system elapsed
## 41.899 1.297 44.676## Inference for Stan model: cd6e07d98bffcf77ad2b924fcd0f1723.
## 4 chains, each with iter=1000; warmup=500; thin=1;
## post-warmup draws per chain=500, total post-warmup draws=2000.
##
## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff
## b0 1.02 0.00 0.06 0.91 0.99 1.02 1.06 1.13 1733
## b1 2.03 0.00 0.07 1.89 1.98 2.03 2.08 2.16 2000
## sigma 0.58 0.00 0.06 0.47 0.53 0.57 0.61 0.70 1557
## lp__ -173.74 0.04 1.21 -177.00 -174.27 -173.43 -172.88 -172.37 1116
## Rhat
## b0 1
## b1 1
## sigma 1
## lp__ 1
##
## Samples were drawn using NUTS(diag_e) at Wed Nov 28 21:29:44 2018.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at
## convergence, Rhat=1).
Wrap-up
Modeling, and Stan
How well a statistical method works depends on the situation.
We can describe the “situation” with a probability model.
Inference usually works best if the probabilistic model reflects reality .
Stan lets you do inference using (almost) arbitrary models.
Explicit models make it easy to simulate, and therefore test your methods.
Hierarchical Bayesian models
It is often possible to infer things about populations that we can’t infer about individuals.
Doing so leads to sharing of information (or, “power”) between samples, and can improve accuracy.
Priors (and hyperpriors) on individual parameters provides a good way to do this.