The logistic model
Peter Ralph
24 November 2020 – Advanced Biological Statistics
The logistic model, a.k.a. “logistic regression”
Motivation
There’s a good bit more information available about the baseball players.
batplus <- read.csv("data/BattingAveragePlus.csv",
header=TRUE, stringsAsFactors=TRUE)
head(batplus)## Player PriPos Hits AtBats PlayerNumber PriPosNumber playerID weight height bats birthYear debut finalGame
## 1 Aaron Cunningham Left Field 17 97 198 7 cunniaa01 215 71 R 1986 2008-08-31 2012-07-24
## 2 Aaron Harang Pitcher 4 56 360 1 haranaa01 260 79 R 1978 2002-05-25 2015-10-03
## 3 Aaron Hill 2nd Base 184 609 394 4 hillaa01 200 71 R 1982 2005-05-20 2016-10-01
## 4 Aaron Laffey Pitcher 0 1 482 1 laffeaa01 190 71 L 1985 2007-08-04 2015-07-31
## 5 Aaron Loup Pitcher 0 1 522 1 loupaa01 210 71 L 1987 2012-07-14 2016-09-30
## 6 Adam Dunn 1st Base 110 539 242 3 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 (\(w_i\)).
Relating values to probabilities
The logistic function
\[\begin{aligned} f(x) = \frac{1}{1 + e^{-x}} . \end{aligned}\]
… is the inverse of the logit function
\[\begin{aligned} f^{-1}(x) = \log\left(\frac{x}{1-x}\right) . \end{aligned}\]
Back to Stan
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 (\(w_i\)).
\[\begin{aligned} Z_i &\sim \Binom(N_i, \theta_i) \\ \theta_i &\sim \Beta(\mu_i \kappa_{p_i}, (1-\mu_i) \kappa_{p_i}) \\ \mu_i &= \logistic(\gamma_{p_i} + \alpha_h h_i + \alpha_w w_i) \\ \kappa_p &\sim \Gam(0.1, 0.1) \\ \gamma_{p} &\sim \Normal(0, 5) \\ \alpha_h &\sim \Normal(0, 5) \\ \alpha_w &\sim \Normal(0, 5) \end{aligned}\]
Questions:
How much do we expect \(\gamma\) to differ for pitchers versus catchers?
What would a value of \(\alpha_h = 1\) mean?
What would be a range of plausible values for \(\alpha_h\) and \(\alpha_w\)?
Are the priors sensible?
Note: we’ll center and scale weight and height, so that \(h\) and \(w\) will be in units of standard deviations from the mean.
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);
} "\[\begin{aligned} Z_i &\sim \Binom(N_i, \theta_i) \\ \theta_i &\sim \Beta(\mu_i \kappa_{p_i}, (1-\mu_i) \kappa_{p_i}) \\ \mu_i &= \logistic(\gamma_{p_i} + \alpha_h h_i + \alpha_w w_i) \\ \kappa_p &\sim \Gam(0.1, 0.1) \\ \gamma_{p} &\sim \Normal(0, 5) \\ \alpha_h &\sim \Normal(0, 5) \\ \alpha_w &\sim \Normal(0, 5) \end{aligned}\]
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.gamma[position]for vectorized indexingx .* 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) ))## Warning: Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.
## Running the chains for more iterations may help. See
## http://mc-stan.org/misc/warnings.html#bulk-ess## Warning: Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.
## Running the chains for more iterations may help. See
## http://mc-stan.org/misc/warnings.html#tail-ess## user system elapsed
## 236.737 3.067 136.295## mean se_mean sd 2.5% 25% 50% 75% 97.5% n_eff Rhat
## theta[1] 2.148156e-01 0.0004895183 0.02991918 1.579063e-01 1.941524e-01 2.138817e-01 2.343610e-01 2.767836e-01 3735.6098 0.9990097
## theta[2] 1.003653e-01 0.0005782312 0.02849696 5.306210e-02 7.991658e-02 9.857809e-02 1.170653e-01 1.636435e-01 2428.8136 0.9988730
## theta[3] 2.944825e-01 0.0002728778 0.01673599 2.616927e-01 2.832199e-01 2.945440e-01 3.054410e-01 3.283094e-01 3761.5452 1.0003648
## theta[4] 1.255611e-01 0.0007781808 0.04611151 5.094841e-02 9.145170e-02 1.192610e-01 1.548317e-01 2.272874e-01 3511.2167 0.9990836
## theta[5] 1.278928e-01 0.0007827714 0.04515064 5.249705e-02 9.585853e-02 1.231579e-01 1.536206e-01 2.305225e-01 3327.0384 0.9982984
## theta[6] 2.135464e-01 0.0002651778 0.01501348 1.841361e-01 2.030753e-01 2.135709e-01 2.241366e-01 2.430412e-01 3205.4433 0.9989146
## theta[7] 2.836905e-01 0.0002475901 0.01666656 2.513674e-01 2.722146e-01 2.834145e-01 2.950135e-01 3.168391e-01 4531.3244 0.9985201
## theta[8] 2.592205e-01 0.0004359554 0.02634874 2.088928e-01 2.409917e-01 2.582475e-01 2.766390e-01 3.104745e-01 3652.8815 0.9982158
## theta[9] 2.679523e-01 0.0003074171 0.01801718 2.334174e-01 2.558237e-01 2.673880e-01 2.796924e-01 3.026122e-01 3434.9272 0.9987408
## theta[10] 2.538053e-01 0.0003556777 0.02010518 2.157586e-01 2.396471e-01 2.532459e-01 2.665435e-01 2.936045e-01 3195.2323 0.9994622
## theta[11] 2.302025e-01 0.0006947231 0.03975017 1.545434e-01 2.031180e-01 2.285270e-01 2.560426e-01 3.094085e-01 3273.8179 0.9983134
## theta[12] 1.263563e-01 0.0006148987 0.04043674 6.195028e-02 9.700767e-02 1.233391e-01 1.500432e-01 2.131228e-01 4324.5922 0.9982843
## theta[13] 2.353829e-01 0.0004840317 0.03048394 1.790708e-01 2.145157e-01 2.330910e-01 2.546901e-01 2.985072e-01 3966.3822 0.9984840
## theta[14] 1.249369e-01 0.0004947384 0.02893057 7.574865e-02 1.039302e-01 1.229870e-01 1.435586e-01 1.850465e-01 3419.5018 0.9982500
## theta[15] 2.541252e-01 0.0004750122 0.03044023 1.961427e-01 2.335936e-01 2.523259e-01 2.742607e-01 3.174373e-01 4106.6382 0.9983306
## theta[16] 3.128254e-01 0.0002522363 0.01647901 2.820343e-01 3.013209e-01 3.127038e-01 3.239244e-01 3.459915e-01 4268.2222 0.9995049
## theta[17] 2.246161e-01 0.0004817428 0.03253286 1.662249e-01 2.029647e-01 2.233196e-01 2.452648e-01 2.921827e-01 4560.5172 0.9983374
## theta[18] 2.915854e-01 0.0002702474 0.01682222 2.596274e-01 2.801131e-01 2.917343e-01 3.032590e-01 3.248219e-01 3874.7503 0.9990705
## theta[19] 2.464460e-01 0.0005610891 0.03669900 1.777676e-01 2.213166e-01 2.461448e-01 2.704123e-01 3.225320e-01 4278.0403 0.9988460
## theta[20] 2.804242e-01 0.0002543573 0.01755643 2.459561e-01 2.685267e-01 2.797559e-01 2.920458e-01 3.157570e-01 4764.1369 0.9988924
## theta[21] 2.536304e-01 0.0002634724 0.01722258 2.207695e-01 2.421085e-01 2.535127e-01 2.651750e-01 2.886077e-01 4272.9339 0.9992759
## theta[22] 2.448342e-01 0.0005812362 0.04011851 1.718933e-01 2.160986e-01 2.428409e-01 2.713018e-01 3.296463e-01 4764.1369 0.9982871
## theta[23] 2.864708e-01 0.0002734237 0.01706008 2.545197e-01 2.748472e-01 2.863169e-01 2.979580e-01 3.203381e-01 3893.0472 1.0002233
## theta[24] 2.774947e-01 0.0002677792 0.01848285 2.412801e-01 2.642910e-01 2.773307e-01 2.898415e-01 3.141294e-01 4764.1369 0.9988126
## theta[25] 2.412510e-01 0.0002783916 0.01921535 2.047796e-01 2.286505e-01 2.407363e-01 2.528449e-01 2.806900e-01 4764.1369 0.9984342
## theta[26] 2.338728e-01 0.0006523662 0.03794735 1.618144e-01 2.079668e-01 2.324794e-01 2.585896e-01 3.096306e-01 3383.6084 0.9986281
## theta[27] 2.880101e-01 0.0002742402 0.01681823 2.565334e-01 2.765935e-01 2.877804e-01 2.992742e-01 3.220582e-01 3760.9587 0.9997072
## theta[28] 1.227010e-01 0.0007901987 0.04380291 5.044460e-02 9.098764e-02 1.190169e-01 1.490381e-01 2.266273e-01 3072.7933 0.9983970
## theta[29] 2.383414e-01 0.0005263577 0.02931153 1.830017e-01 2.188387e-01 2.385015e-01 2.567642e-01 2.973502e-01 3101.0947 0.9992676
## theta[30] 2.388247e-01 0.0003362131 0.01997761 2.019232e-01 2.249391e-01 2.383684e-01 2.524366e-01 2.781579e-01 3530.6769 0.9990945
## theta[31] 2.961167e-01 0.0002564842 0.01770324 2.610573e-01 2.839316e-01 2.959745e-01 3.077493e-01 3.310704e-01 4764.1369 0.9983916
## theta[32] 2.697734e-01 0.0002909197 0.01858983 2.334089e-01 2.570431e-01 2.697690e-01 2.818372e-01 3.081321e-01 4083.2347 0.9993904
## theta[33] 1.456823e-01 0.0006856722 0.03910784 7.712402e-02 1.180785e-01 1.433942e-01 1.715518e-01 2.310906e-01 3253.0789 0.9993149
## theta[34] 2.618153e-01 0.0002577640 0.01613493 2.313864e-01 2.504122e-01 2.617284e-01 2.729697e-01 2.929005e-01 3918.2258 0.9985134
## theta[35] 2.418529e-01 0.0003196474 0.02206293 2.003181e-01 2.271608e-01 2.416241e-01 2.565061e-01 2.843876e-01 4764.1369 0.9986727
## theta[36] 2.426113e-01 0.0003009631 0.02077329 2.041988e-01 2.283954e-01 2.422236e-01 2.568515e-01 2.838260e-01 4764.1369 0.9982894
## theta[37] 1.417141e-01 0.0007040871 0.04780257 6.129505e-02 1.076241e-01 1.374430e-01 1.700717e-01 2.499797e-01 4609.4570 0.9990695
## theta[38] 2.590063e-01 0.0002394590 0.01652812 2.289967e-01 2.476398e-01 2.587624e-01 2.696099e-01 2.922782e-01 4764.1369 0.9990901
## theta[39] 1.231167e-01 0.0009508699 0.04429075 5.030158e-02 9.164862e-02 1.185251e-01 1.500981e-01 2.199042e-01 2169.6211 0.9997138
## theta[40] 2.252669e-01 0.0007078722 0.04343171 1.446643e-01 1.953119e-01 2.249632e-01 2.539143e-01 3.130284e-01 3764.4716 0.9986233
## theta[41] 2.966982e-01 0.0003190760 0.01889772 2.606341e-01 2.834475e-01 2.957446e-01 3.093584e-01 3.341781e-01 3507.7670 0.9986605
## theta[42] 2.800137e-01 0.0002720628 0.01735825 2.467566e-01 2.682142e-01 2.803111e-01 2.913138e-01 3.145935e-01 4070.7424 0.9988484
## theta[43] 2.738120e-01 0.0004265208 0.02662805 2.265596e-01 2.549690e-01 2.726269e-01 2.923491e-01 3.265809e-01 3897.6104 0.9997920
## theta[44] 2.360664e-01 0.0003227316 0.01988142 1.980684e-01 2.219989e-01 2.354544e-01 2.491906e-01 2.759285e-01 3795.0000 0.9983184
## theta[45] 1.311846e-01 0.0006945257 0.04370000 5.963132e-02 9.966852e-02 1.275127e-01 1.585311e-01 2.287269e-01 3959.0067 0.9990690
## theta[46] 3.173537e-01 0.0002732614 0.01762932 2.825278e-01 3.054994e-01 3.173236e-01 3.285102e-01 3.516024e-01 4162.1197 0.9981746
## theta[47] 2.743949e-01 0.0006768035 0.04328219 1.979141e-01 2.407788e-01 2.724943e-01 3.056265e-01 3.592689e-01 4089.7184 0.9986090
## theta[48] 1.202553e-01 0.0008415973 0.04250509 4.804709e-02 9.048247e-02 1.163353e-01 1.454381e-01 2.136034e-01 2550.7811 0.9991009
## theta[49] 2.143409e-01 0.0003527644 0.02265912 1.705957e-01 1.981160e-01 2.137672e-01 2.296824e-01 2.607314e-01 4125.8809 0.9984999
## theta[50] 3.025962e-01 0.0003583224 0.02334924 2.573972e-01 2.871280e-01 3.022618e-01 3.180193e-01 3.491529e-01 4246.1735 0.9986146
## theta[51] 2.231825e-01 0.0004445688 0.03012408 1.651169e-01 2.035366e-01 2.222644e-01 2.429722e-01 2.899500e-01 4591.4457 0.9987441
## theta[52] 1.394733e-01 0.0007453655 0.04626455 6.183264e-02 1.056483e-01 1.341732e-01 1.702834e-01 2.407768e-01 3852.6377 0.9982615
## theta[53] 1.473784e-01 0.0008598911 0.04795848 6.634468e-02 1.140302e-01 1.418517e-01 1.780897e-01 2.524741e-01 3110.5982 0.9985267
## theta[54] 2.835438e-01 0.0002530672 0.01612968 2.528448e-01 2.724174e-01 2.834438e-01 2.943841e-01 3.152176e-01 4062.3742 0.9993353
## theta[55] 1.188894e-01 0.0005131504 0.03532720 5.702777e-02 9.444435e-02 1.150302e-01 1.413945e-01 1.992335e-01 4739.4610 0.9982969
## theta[56] 1.284514e-01 0.0005487340 0.03787512 6.454169e-02 1.007488e-01 1.247081e-01 1.541705e-01 2.127926e-01 4764.1369 0.9980870
## theta[57] 2.355839e-01 0.0004419872 0.02643808 1.865824e-01 2.172894e-01 2.354648e-01 2.525819e-01 2.906654e-01 3578.0011 0.9982345
## theta[58] 2.054986e-01 0.0006188904 0.03565836 1.402104e-01 1.814859e-01 2.045150e-01 2.279271e-01 2.789900e-01 3319.6734 0.9984550
## theta[59] 2.775778e-01 0.0003231110 0.02101754 2.383291e-01 2.626773e-01 2.772619e-01 2.914784e-01 3.198165e-01 4231.1697 0.9986459
## theta[60] 1.241239e-01 0.0007191626 0.04526554 4.694260e-02 9.202436e-02 1.194720e-01 1.515547e-01 2.265454e-01 3961.6968 0.9989143
## theta[61] 2.936436e-01 0.0002630827 0.01815868 2.598687e-01 2.808332e-01 2.930158e-01 3.051062e-01 3.310475e-01 4764.1369 0.9991876
## theta[62] 1.129436e-01 0.0007200344 0.04097063 4.128756e-02 8.392704e-02 1.102921e-01 1.394576e-01 2.025429e-01 3237.7165 0.9990309
## theta[63] 2.675029e-01 0.0002481627 0.01712887 2.343934e-01 2.559581e-01 2.666698e-01 2.788718e-01 3.022051e-01 4764.1369 0.9991385
## theta[64] 2.264446e-01 0.0005657411 0.03194867 1.665087e-01 2.059441e-01 2.260096e-01 2.466526e-01 2.909042e-01 3189.1144 1.0001042
## theta[65] 2.939541e-01 0.0002682420 0.01806560 2.600909e-01 2.807555e-01 2.939739e-01 3.067048e-01 3.295555e-01 4535.7721 0.9985052
## theta[66] 2.480339e-01 0.0004456061 0.02806615 1.963473e-01 2.279163e-01 2.474780e-01 2.665051e-01 3.044814e-01 3967.0119 0.9981997
## theta[67] 2.800250e-01 0.0006203693 0.03580532 2.159230e-01 2.552549e-01 2.782087e-01 3.024595e-01 3.565259e-01 3331.1529 0.9984008
## theta[68] 1.269952e-01 0.0008285471 0.04636476 4.914271e-02 9.390073e-02 1.220007e-01 1.539443e-01 2.275560e-01 3131.4228 0.9986187
## theta[69] 1.025411e-01 0.0005177453 0.02805650 5.341607e-02 8.191166e-02 1.010054e-01 1.200346e-01 1.624369e-01 2936.5302 1.0000114
## theta[70] 1.299397e-01 0.0008068211 0.04347660 5.465151e-02 9.803026e-02 1.273123e-01 1.577962e-01 2.228128e-01 2903.7327 0.9985063
## theta[71] 2.453333e-01 0.0004217961 0.02566063 1.964388e-01 2.267825e-01 2.442170e-01 2.634844e-01 2.958160e-01 3701.0882 0.9984472
## theta[72] 2.868749e-01 0.0003084242 0.01784310 2.526916e-01 2.747670e-01 2.869767e-01 2.988057e-01 3.221165e-01 3346.9084 1.0001127
## theta[73] 1.027027e-01 0.0006737368 0.03692981 4.139076e-02 7.537230e-02 9.930110e-02 1.264689e-01 1.833217e-01 3004.5093 0.9990596
## theta[74] 2.677906e-01 0.0002759243 0.01666522 2.361646e-01 2.567506e-01 2.675015e-01 2.785961e-01 3.021808e-01 3647.8937 0.9983489
## theta[75] 3.048784e-01 0.0002689506 0.01777920 2.711461e-01 2.923380e-01 3.043039e-01 3.172483e-01 3.406105e-01 4369.9784 0.9998833
## theta[76] 1.248872e-01 0.0008098992 0.04538575 4.898493e-02 9.247283e-02 1.212354e-01 1.512640e-01 2.271183e-01 3140.3434 0.9999766
## theta[77] 2.237273e-01 0.0005871351 0.03631161 1.548356e-01 1.984144e-01 2.233474e-01 2.477516e-01 2.948667e-01 3824.8555 0.9981112
## theta[78] 2.217187e-01 0.0007572510 0.04183091 1.443892e-01 1.937449e-01 2.195619e-01 2.494124e-01 3.058397e-01 3051.5108 0.9991855
## theta[79] 2.293085e-01 0.0007167123 0.03978354 1.542617e-01 2.016216e-01 2.280353e-01 2.555077e-01 3.106522e-01 3081.1806 0.9983459
## theta[80] 2.451731e-01 0.0003534476 0.02396271 2.003307e-01 2.287153e-01 2.448610e-01 2.607362e-01 2.927785e-01 4596.4440 0.9982291
## theta[81] 2.216953e-01 0.0004237430 0.02637650 1.717876e-01 2.033104e-01 2.211993e-01 2.396562e-01 2.728180e-01 3874.6194 0.9984367
## theta[82] 1.254182e-01 0.0008152490 0.04720930 4.770867e-02 9.206188e-02 1.218511e-01 1.510582e-01 2.344342e-01 3353.3166 0.9989944
## theta[83] 1.269608e-01 0.0008078908 0.04451516 5.060005e-02 9.649412e-02 1.226792e-01 1.548528e-01 2.223157e-01 3036.0610 0.9988294
## theta[84] 1.272239e-01 0.0008618779 0.04549658 5.429743e-02 9.560059e-02 1.230953e-01 1.545115e-01 2.308502e-01 2786.5453 1.0003719
## theta[85] 1.425130e-01 0.0007623837 0.04637946 6.416508e-02 1.097281e-01 1.386878e-01 1.707344e-01 2.479029e-01 3700.8723 0.9985190
## theta[86] 1.330859e-01 0.0007899237 0.04780435 5.336123e-02 9.850003e-02 1.287876e-01 1.614197e-01 2.384298e-01 3662.3898 0.9991588
## theta[87] 1.372435e-01 0.0006913372 0.04661237 5.786842e-02 1.050287e-01 1.330993e-01 1.661456e-01 2.387007e-01 4545.9286 0.9984520
## theta[88] 2.290746e-01 0.0007081903 0.03912733 1.557650e-01 2.003840e-01 2.283878e-01 2.548978e-01 3.106841e-01 3052.5336 0.9998452
## theta[89] 2.301753e-01 0.0004804909 0.03010135 1.724990e-01 2.089427e-01 2.296522e-01 2.498668e-01 2.888883e-01 3924.6543 0.9996945
## theta[90] 1.480765e-01 0.0007973313 0.04065247 7.691116e-02 1.186411e-01 1.442112e-01 1.735109e-01 2.349868e-01 2599.5378 0.9996598
## theta[91] 2.694459e-01 0.0003217288 0.01858503 2.348709e-01 2.565732e-01 2.690818e-01 2.828281e-01 3.047506e-01 3336.9273 0.9982544
## theta[92] 2.488017e-01 0.0002764496 0.01908130 2.118687e-01 2.363140e-01 2.486293e-01 2.613783e-01 2.856984e-01 4764.1369 0.9986252
## theta[93] 1.382617e-01 0.0007201730 0.04543978 6.277411e-02 1.043459e-01 1.334351e-01 1.667764e-01 2.423030e-01 3981.0602 0.9984184
## theta[94] 1.243886e-01 0.0008932694 0.04315250 4.969674e-02 9.369534e-02 1.215002e-01 1.500872e-01 2.183947e-01 2333.7102 0.9999407
## theta[95] 2.383086e-01 0.0006693320 0.04226064 1.613432e-01 2.092728e-01 2.364363e-01 2.655277e-01 3.270719e-01 3986.4742 0.9991309
## theta[96] 2.168611e-01 0.0006258721 0.03471179 1.518538e-01 1.930570e-01 2.154739e-01 2.389488e-01 2.877998e-01 3075.9760 0.9996366
## theta[97] 2.263380e-01 0.0003291590 0.02125565 1.856952e-01 2.116718e-01 2.258638e-01 2.411571e-01 2.688553e-01 4170.0119 0.9982772
## theta[98] 2.565819e-01 0.0005320459 0.03672326 1.895082e-01 2.315132e-01 2.552982e-01 2.806792e-01 3.306605e-01 4764.1369 0.9985794
## theta[99] 2.800333e-01 0.0003716002 0.02388874 2.339970e-01 2.636171e-01 2.798598e-01 2.960709e-01 3.265039e-01 4132.7056 0.9995133
## theta[100] 2.766057e-01 0.0002710583 0.01698140 2.454160e-01 2.641489e-01 2.764726e-01 2.887692e-01 3.105495e-01 3924.8357 0.9983188
## theta[101] 2.617811e-01 0.0005144950 0.03551184 1.937472e-01 2.371229e-01 2.611991e-01 2.837984e-01 3.355619e-01 4764.1369 0.9987577
## theta[102] 2.384914e-01 0.0003701156 0.02384025 1.938387e-01 2.213385e-01 2.381882e-01 2.551293e-01 2.867276e-01 4149.0331 0.9989994
## theta[103] 2.034011e-01 0.0003067035 0.01884601 1.683710e-01 1.905530e-01 2.031723e-01 2.159184e-01 2.413270e-01 3775.7367 0.9982351
## theta[104] 2.437055e-01 0.0003515658 0.01709847 2.104320e-01 2.318011e-01 2.435095e-01 2.552357e-01 2.774022e-01 2365.3821 0.9993639
## theta[105] 2.142914e-01 0.0003508359 0.02348932 1.701892e-01 1.979287e-01 2.134990e-01 2.298517e-01 2.610024e-01 4482.6277 0.9991653
## theta[106] 2.139075e-01 0.0005038724 0.02758813 1.633526e-01 1.939071e-01 2.126369e-01 2.332065e-01 2.681885e-01 2997.8047 1.0000582
## theta[107] 2.558421e-01 0.0007313209 0.04616550 1.708975e-01 2.243928e-01 2.539676e-01 2.849448e-01 3.529428e-01 3984.9150 0.9983328
## theta[108] 1.246545e-01 0.0008335468 0.04325192 5.295511e-02 9.296449e-02 1.193511e-01 1.525437e-01 2.185548e-01 2692.4700 1.0002430
## theta[109] 2.651361e-01 0.0006189539 0.03982500 1.888879e-01 2.386426e-01 2.637540e-01 2.904355e-01 3.488404e-01 4139.9493 0.9985609
## theta[110] 2.169081e-01 0.0004692830 0.03085331 1.598795e-01 1.960215e-01 2.159536e-01 2.375250e-01 2.798887e-01 4322.4899 0.9986519
## theta[111] 2.113804e-01 0.0005051817 0.02776300 1.590297e-01 1.926480e-01 2.099038e-01 2.285364e-01 2.685726e-01 3020.2132 0.9981766
## theta[112] 2.707136e-01 0.0002912037 0.01854927 2.357087e-01 2.578368e-01 2.702956e-01 2.832831e-01 3.073926e-01 4057.5113 0.9995255
## theta[113] 2.305745e-01 0.0005150870 0.02949486 1.754356e-01 2.111762e-01 2.295545e-01 2.485191e-01 2.903693e-01 3278.9252 0.9990621
## theta[114] 2.554255e-01 0.0003753053 0.02387359 2.117867e-01 2.388231e-01 2.545922e-01 2.717641e-01 3.023204e-01 4046.3757 0.9987802
## theta[115] 2.280951e-01 0.0005036602 0.03042390 1.715459e-01 2.080327e-01 2.267327e-01 2.471664e-01 2.906208e-01 3648.8389 0.9988553
## theta[116] 2.156910e-01 0.0003245950 0.01936168 1.788994e-01 2.027326e-01 2.154419e-01 2.276796e-01 2.560892e-01 3557.9716 0.9992510
## theta[117] 2.371310e-01 0.0003929581 0.02244336 1.954341e-01 2.215740e-01 2.360166e-01 2.519029e-01 2.846217e-01 3261.9955 0.9984412
## theta[118] 1.248841e-01 0.0008195407 0.04497881 5.205379e-02 9.403334e-02 1.202402e-01 1.506682e-01 2.281175e-01 3012.1373 0.9993748
## theta[119] 1.340161e-01 0.0007453743 0.04656636 5.877304e-02 1.010737e-01 1.293309e-01 1.610573e-01 2.417291e-01 3902.9747 0.9985110
## theta[120] 2.310264e-01 0.0002843499 0.01908933 1.950168e-01 2.181000e-01 2.303282e-01 2.433015e-01 2.698691e-01 4506.8724 0.9982730
## theta[121] 2.208717e-01 0.0004890882 0.03122115 1.617332e-01 1.995131e-01 2.193912e-01 2.409505e-01 2.850929e-01 4074.9613 0.9984187
## theta[122] 1.241274e-01 0.0007661363 0.04535574 5.193559e-02 9.195856e-02 1.194732e-01 1.499705e-01 2.232347e-01 3504.7136 0.9983090
## theta[123] 2.313461e-01 0.0004673528 0.03179982 1.738005e-01 2.086321e-01 2.312482e-01 2.527934e-01 2.953953e-01 4629.7711 0.9982533
## theta[124] 2.652723e-01 0.0005966552 0.03413988 2.025122e-01 2.406326e-01 2.637593e-01 2.885966e-01 3.341587e-01 3273.9877 0.9992765
## theta[125] 1.342247e-01 0.0004657618 0.03186791 7.885074e-02 1.120988e-01 1.312946e-01 1.558050e-01 2.002268e-01 4681.4400 0.9990943
## theta[126] 1.926924e-01 0.0005369299 0.02889061 1.383301e-01 1.736467e-01 1.911191e-01 2.116833e-01 2.502482e-01 2895.1978 0.9992257
## theta[127] 1.384421e-01 0.0007126448 0.04356157 6.558720e-02 1.068567e-01 1.349910e-01 1.634586e-01 2.387735e-01 3736.4640 0.9989817
## theta[128] 1.354695e-01 0.0007596080 0.04355516 6.209941e-02 1.052702e-01 1.313508e-01 1.609135e-01 2.353086e-01 3287.7603 0.9993282
## theta[129] 2.366090e-01 0.0007792432 0.04330861 1.541616e-01 2.062104e-01 2.349884e-01 2.647554e-01 3.227730e-01 3088.8901 0.9984681
## theta[130] 2.371421e-01 0.0007199611 0.04443972 1.551185e-01 2.066337e-01 2.346922e-01 2.645899e-01 3.321110e-01 3809.9952 0.9984226
## theta[131] 2.583588e-01 0.0003394219 0.02033921 2.192270e-01 2.436468e-01 2.580215e-01 2.729923e-01 2.972377e-01 3590.7774 0.9999317
## theta[132] 2.113260e-01 0.0004091883 0.02389713 1.663752e-01 1.947236e-01 2.102724e-01 2.275515e-01 2.616451e-01 3410.7131 0.9993138
## theta[133] 2.686168e-01 0.0002515298 0.01736127 2.351968e-01 2.576062e-01 2.679804e-01 2.793082e-01 3.042747e-01 4764.1369 0.9984422
## theta[134] 1.152409e-01 0.0005449666 0.03155617 6.047289e-02 9.330696e-02 1.125110e-01 1.341497e-01 1.846623e-01 3352.9636 0.9982807
## theta[135] 1.235670e-01 0.0008657364 0.04357725 4.837017e-02 9.323998e-02 1.198313e-01 1.493345e-01 2.201363e-01 2533.6590 0.9997606
## theta[136] 3.218628e-01 0.0003618823 0.01885265 2.862761e-01 3.088789e-01 3.222879e-01 3.351510e-01 3.586395e-01 2714.0029 0.9984247
## theta[137] 2.446677e-01 0.0002654205 0.01730586 2.116746e-01 2.324880e-01 2.447091e-01 2.559897e-01 2.792951e-01 4251.2574 0.9991146
## theta[138] 2.684608e-01 0.0004584827 0.02989925 2.129867e-01 2.475183e-01 2.680667e-01 2.873285e-01 3.279793e-01 4252.7976 0.9985384
## theta[139] 1.288180e-01 0.0007682145 0.04530756 5.201992e-02 9.629261e-02 1.247221e-01 1.572148e-01 2.239102e-01 3478.3747 0.9986039
## theta[140] 2.673878e-01 0.0002630620 0.01815726 2.318321e-01 2.556415e-01 2.667847e-01 2.790862e-01 3.040985e-01 4764.1369 0.9982904
## theta[141] 2.544399e-01 0.0005106085 0.03344477 1.908569e-01 2.313506e-01 2.532513e-01 2.767911e-01 3.196207e-01 4290.2283 0.9989055
## theta[142] 2.598866e-01 0.0003722413 0.01917928 2.224149e-01 2.469604e-01 2.591543e-01 2.729113e-01 2.981241e-01 2654.7001 0.9986501
## theta[143] 2.944245e-01 0.0003311521 0.01862275 2.597735e-01 2.817179e-01 2.935913e-01 3.069646e-01 3.304459e-01 3162.5148 0.9982917
## theta[144] 2.630806e-01 0.0002705147 0.01695946 2.304965e-01 2.516122e-01 2.625169e-01 2.747139e-01 2.965746e-01 3930.4472 0.9998460
## theta[145] 2.356239e-01 0.0005575673 0.03312956 1.734124e-01 2.125359e-01 2.352337e-01 2.579525e-01 3.013303e-01 3530.5040 0.9985408
## theta[146] 2.074130e-01 0.0002633085 0.01628773 1.756844e-01 1.969305e-01 2.074001e-01 2.178996e-01 2.404539e-01 3826.4090 0.9992290
## theta[147] 2.583457e-01 0.0003316022 0.02117934 2.180207e-01 2.440062e-01 2.581459e-01 2.728420e-01 2.994852e-01 4079.3418 0.9981743
## theta[148] 3.085548e-01 0.0003150781 0.02174755 2.655557e-01 2.940789e-01 3.086080e-01 3.228403e-01 3.524010e-01 4764.1369 0.9981387
## theta[149] 2.504910e-01 0.0002742248 0.01791039 2.170617e-01 2.386165e-01 2.498170e-01 2.624721e-01 2.857961e-01 4265.7629 0.9995610
## theta[150] 1.388638e-01 0.0007343927 0.04525776 6.410196e-02 1.077962e-01 1.346148e-01 1.640811e-01 2.406567e-01 3797.7767 0.9984956
## theta[151] 2.429546e-01 0.0006455516 0.04090796 1.671578e-01 2.155615e-01 2.413625e-01 2.685447e-01 3.259799e-01 4015.6310 0.9990789
## theta[152] 1.435146e-01 0.0009099662 0.04921090 6.108084e-02 1.082402e-01 1.384538e-01 1.752386e-01 2.529895e-01 2924.6379 0.9995022
## theta[153] 1.510944e-01 0.0006541044 0.03929415 8.395579e-02 1.229027e-01 1.481379e-01 1.774130e-01 2.372577e-01 3608.7897 0.9983203
## theta[154] 1.377037e-01 0.0009059988 0.04595571 6.044788e-02 1.057527e-01 1.330195e-01 1.664038e-01 2.365258e-01 2572.9044 0.9992340
## theta[155] 1.396550e-01 0.0008427743 0.04335453 6.506546e-02 1.091767e-01 1.368263e-01 1.665437e-01 2.327944e-01 2646.3444 0.9994419
## theta[156] 2.329972e-01 0.0002814781 0.01809539 1.979761e-01 2.211910e-01 2.326211e-01 2.444031e-01 2.706961e-01 4132.8220 0.9981873
## theta[157] 2.263747e-01 0.0003141744 0.02073466 1.877484e-01 2.121372e-01 2.266873e-01 2.400211e-01 2.681153e-01 4355.6411 0.9985919
## theta[158] 2.336921e-01 0.0003275216 0.02155844 1.931603e-01 2.185853e-01 2.335871e-01 2.482640e-01 2.767616e-01 4332.6587 0.9984163
## theta[159] 1.253442e-01 0.0008115937 0.04365165 4.618252e-02 9.499679e-02 1.233229e-01 1.516847e-01 2.211084e-01 2892.8367 0.9997909
## theta[160] 2.418913e-01 0.0004865676 0.02748686 1.896815e-01 2.234953e-01 2.410358e-01 2.594227e-01 2.967233e-01 3191.2736 0.9987547
## theta[161] 1.244582e-01 0.0008877283 0.04595808 4.788518e-02 9.272460e-02 1.198235e-01 1.499398e-01 2.289167e-01 2680.1785 0.9987179
## theta[162] 1.577045e-01 0.0006144532 0.03733826 9.346281e-02 1.310447e-01 1.540523e-01 1.818490e-01 2.385134e-01 3692.5843 0.9986167
## theta[163] 1.098907e-01 0.0008061449 0.03904311 4.486603e-02 8.113544e-02 1.060512e-01 1.348218e-01 1.953483e-01 2345.6466 0.9984285
## theta[164] 2.588849e-01 0.0005918570 0.03190936 1.972738e-01 2.365023e-01 2.585659e-01 2.795444e-01 3.224415e-01 2906.7161 0.9997722
## theta[165] 2.702625e-01 0.0004811626 0.03018272 2.146828e-01 2.484545e-01 2.696206e-01 2.894331e-01 3.299724e-01 3934.8918 0.9988573
## theta[166] 2.288778e-01 0.0006945993 0.04022754 1.490256e-01 2.019737e-01 2.295360e-01 2.539340e-01 3.126897e-01 3354.1168 0.9989411
## theta[167] 2.822768e-01 0.0002560018 0.01734184 2.512971e-01 2.697341e-01 2.817336e-01 2.941487e-01 3.170606e-01 4588.8518 0.9991832
## theta[168] 2.534396e-01 0.0003887575 0.02091827 2.145612e-01 2.383521e-01 2.537575e-01 2.672489e-01 2.942162e-01 2895.3011 0.9992064
## theta[169] 2.797716e-01 0.0003266464 0.02156954 2.378540e-01 2.659722e-01 2.791540e-01 2.936191e-01 3.229082e-01 4360.3952 0.9990125
## theta[170] 2.062392e-01 0.0004568879 0.02539556 1.591192e-01 1.891387e-01 2.059837e-01 2.228179e-01 2.561196e-01 3089.5577 0.9988015
## theta[171] 1.189510e-01 0.0007526229 0.04278823 4.658592e-02 8.884400e-02 1.155564e-01 1.455384e-01 2.152651e-01 3232.1676 0.9985606
## theta[172] 1.116873e-01 0.0004541377 0.03012882 6.045624e-02 9.003521e-02 1.087290e-01 1.314970e-01 1.763764e-01 4401.3839 0.9983024
## theta[173] 1.957954e-01 0.0005531513 0.03000051 1.400512e-01 1.741508e-01 1.960545e-01 2.161966e-01 2.546082e-01 2941.5044 0.9997054
## theta[174] 2.669430e-01 0.0002550641 0.01734029 2.336534e-01 2.547029e-01 2.666619e-01 2.786225e-01 3.017518e-01 4621.8292 0.9987825
## theta[175] 2.847129e-01 0.0003896594 0.02119386 2.440819e-01 2.713172e-01 2.841322e-01 2.980504e-01 3.289066e-01 2958.3531 0.9983889
## theta[176] 2.543678e-01 0.0005732078 0.03956437 1.815124e-01 2.265555e-01 2.531304e-01 2.796812e-01 3.374945e-01 4764.1369 0.9992207
## theta[177] 2.650859e-01 0.0004142017 0.02640779 2.166323e-01 2.465395e-01 2.639742e-01 2.830355e-01 3.172975e-01 4064.8122 0.9991671
## theta[178] 2.508398e-01 0.0005020196 0.03168368 1.920870e-01 2.293100e-01 2.499081e-01 2.717245e-01 3.150664e-01 3983.1800 0.9986560
## theta[179] 2.616372e-01 0.0003144287 0.02170272 2.198171e-01 2.472893e-01 2.611518e-01 2.757876e-01 3.060825e-01 4764.1369 0.9985094
## theta[180] 2.045589e-01 0.0007567452 0.03940755 1.326938e-01 1.756921e-01 2.035733e-01 2.308107e-01 2.854383e-01 2711.8117 0.9995833
## theta[181] 2.406267e-01 0.0003552439 0.02451990 1.961493e-01 2.233277e-01 2.391495e-01 2.570865e-01 2.899780e-01 4764.1369 0.9987719
## theta[182] 2.778337e-01 0.0002928026 0.01924442 2.402040e-01 2.655302e-01 2.777958e-01 2.904343e-01 3.162189e-01 4319.7632 0.9993791
## theta[183] 1.251458e-01 0.0007706001 0.04345620 5.153065e-02 9.288879e-02 1.210279e-01 1.538385e-01 2.172239e-01 3180.1330 0.9995943
## theta[184] 1.214584e-01 0.0008438483 0.04588188 4.659776e-02 8.847629e-02 1.173452e-01 1.474509e-01 2.269228e-01 2956.3346 0.9990399
## theta[185] 2.918699e-01 0.0003322631 0.02210702 2.467856e-01 2.780277e-01 2.916497e-01 3.049170e-01 3.388097e-01 4426.8625 0.9993258
## theta[186] 2.381909e-01 0.0003740608 0.02335214 1.936813e-01 2.216531e-01 2.375502e-01 2.538432e-01 2.853562e-01 3897.3476 0.9997425
## theta[187] 1.230341e-01 0.0008376345 0.04375796 4.958861e-02 9.272914e-02 1.193099e-01 1.485930e-01 2.243544e-01 2729.0099 0.9999060
## theta[188] 1.354419e-01 0.0007693429 0.04343834 6.355575e-02 1.037051e-01 1.310389e-01 1.632132e-01 2.327275e-01 3187.9138 0.9984652
## theta[189] 1.194091e-01 0.0008294711 0.04386378 4.703776e-02 8.776985e-02 1.153360e-01 1.439175e-01 2.194401e-01 2796.4668 0.9997875
## theta[190] 1.373828e-01 0.0008951696 0.04723381 5.661710e-02 1.053518e-01 1.341297e-01 1.654074e-01 2.479922e-01 2784.1677 0.9983515
## theta[191] 1.942344e-01 0.0004062442 0.02305679 1.516267e-01 1.776327e-01 1.931254e-01 2.101423e-01 2.404275e-01 3221.2418 0.9983555
## theta[192] 2.375548e-01 0.0004715056 0.02824954 1.863198e-01 2.181495e-01 2.366424e-01 2.554736e-01 2.958354e-01 3589.6245 0.9985903
## theta[193] 1.455757e-01 0.0006593759 0.03881990 7.814669e-02 1.177595e-01 1.419762e-01 1.706396e-01 2.301034e-01 3466.1139 0.9986027
## theta[194] 1.125352e-01 0.0007480146 0.03626401 4.950956e-02 8.759843e-02 1.089527e-01 1.350540e-01 1.933370e-01 2350.3443 0.9998751
## theta[195] 1.218743e-01 0.0007946033 0.04327852 5.140985e-02 9.127000e-02 1.176219e-01 1.478854e-01 2.191714e-01 2966.4980 0.9989555
## theta[196] 1.264249e-01 0.0007345557 0.04707159 4.922531e-02 9.364150e-02 1.208398e-01 1.540057e-01 2.329783e-01 4106.4672 0.9984980
## theta[197] 1.686125e-01 0.0006696568 0.03601405 1.067475e-01 1.426285e-01 1.669042e-01 1.918756e-01 2.464692e-01 2892.2730 0.9984270
## theta[198] 1.223673e-01 0.0008027756 0.04526063 5.075396e-02 8.884966e-02 1.178192e-01 1.500961e-01 2.264259e-01 3178.7240 0.9986044
## theta[199] 1.058676e-01 0.0004587610 0.02704702 5.834475e-02 8.599494e-02 1.041658e-01 1.234263e-01 1.629648e-01 3475.8877 0.9995852
## theta[200] 2.348203e-01 0.0006719083 0.03635229 1.668292e-01 2.096077e-01 2.342469e-01 2.582074e-01 3.103842e-01 2927.1402 0.9994161
## theta[201] 2.209065e-01 0.0003017410 0.01822248 1.849521e-01 2.092028e-01 2.202947e-01 2.328176e-01 2.562664e-01 3647.0890 0.9988369
## theta[202] 2.314875e-01 0.0002905852 0.01712976 1.988775e-01 2.205730e-01 2.316890e-01 2.423825e-01 2.652991e-01 3475.0073 0.9992363
## theta[203] 2.585916e-01 0.0002965202 0.01849977 2.221955e-01 2.465041e-01 2.586072e-01 2.704082e-01 2.941959e-01 3892.4606 0.9990602
## theta[204] 2.267569e-01 0.0004211585 0.02202103 1.836356e-01 2.123917e-01 2.263760e-01 2.411903e-01 2.739504e-01 2733.9084 0.9983966
## theta[205] 2.648813e-01 0.0003076801 0.01813707 2.299072e-01 2.525336e-01 2.648901e-01 2.767638e-01 3.020514e-01 3474.8439 0.9982089
## theta[206] 1.561108e-01 0.0008564995 0.04872176 7.742515e-02 1.216432e-01 1.516216e-01 1.851754e-01 2.608467e-01 3235.8752 0.9989712
## theta[207] 2.282584e-01 0.0002402486 0.01658261 1.953950e-01 2.170627e-01 2.277467e-01 2.386799e-01 2.607002e-01 4764.1369 0.9985887
## theta[208] 1.778791e-01 0.0006127444 0.03482313 1.143161e-01 1.528025e-01 1.768034e-01 2.011131e-01 2.511238e-01 3229.8102 0.9986416
## theta[209] 2.583278e-01 0.0005202474 0.02963446 2.023151e-01 2.382140e-01 2.572698e-01 2.783862e-01 3.187587e-01 3244.6979 0.9998711
## theta[210] 1.164270e-01 0.0007391893 0.04093009 4.677084e-02 8.810979e-02 1.133820e-01 1.399542e-01 2.089434e-01 3066.0139 0.9992154
## theta[211] 2.345865e-01 0.0005704277 0.03937247 1.630789e-01 2.068143e-01 2.330363e-01 2.605877e-01 3.171044e-01 4764.1369 0.9985237
## theta[212] 2.405245e-01 0.0005878014 0.03573586 1.720054e-01 2.154263e-01 2.389002e-01 2.650340e-01 3.112240e-01 3696.1289 0.9984409
## theta[213] 2.368483e-01 0.0006004628 0.03793548 1.610971e-01 2.112890e-01 2.369090e-01 2.609814e-01 3.147546e-01 3991.3419 0.9989983
## theta[214] 2.676648e-01 0.0003046298 0.01714035 2.353685e-01 2.554355e-01 2.675770e-01 2.792136e-01 3.014711e-01 3165.8797 0.9984291
## theta[215] 1.271464e-01 0.0008441040 0.04995651 4.713332e-02 9.067914e-02 1.221360e-01 1.564663e-01 2.418361e-01 3502.6141 0.9980859
## theta[216] 1.063790e-01 0.0008138916 0.04104865 4.095088e-02 7.769946e-02 1.021292e-01 1.307714e-01 1.980151e-01 2543.6924 0.9989126
## theta[217] 1.188839e-01 0.0006903602 0.04321599 4.976033e-02 8.643587e-02 1.138629e-01 1.447100e-01 2.137889e-01 3918.6582 0.9985526
## theta[218] 2.899461e-01 0.0003680074 0.02540087 2.436125e-01 2.728314e-01 2.894959e-01 3.063476e-01 3.399563e-01 4764.1369 0.9987550
## theta[219] 1.165643e-01 0.0007958861 0.04216941 4.623850e-02 8.630149e-02 1.140525e-01 1.406774e-01 2.084876e-01 2807.3292 0.9985638
## theta[220] 1.189312e-01 0.0006990859 0.04311983 4.724388e-02 8.811608e-02 1.149342e-01 1.459138e-01 2.147736e-01 3804.4599 0.9987872
## theta[221] 2.349584e-01 0.0002502821 0.01648126 2.030813e-01 2.239410e-01 2.353038e-01 2.453807e-01 2.681091e-01 4336.3216 0.9987921
## theta[222] 1.233221e-01 0.0007924085 0.04514770 4.646508e-02 9.124675e-02 1.187844e-01 1.530235e-01 2.250031e-01 3246.1829 0.9986307
## theta[223] 1.190051e-01 0.0006793279 0.03712286 5.677319e-02 9.227082e-02 1.153799e-01 1.441791e-01 1.987882e-01 2986.2352 0.9989266
## theta[224] 1.175907e-01 0.0007992902 0.04497903 4.560478e-02 8.721679e-02 1.128084e-01 1.436629e-01 2.179919e-01 3166.7314 0.9998826
## theta[225] 1.258130e-01 0.0008466671 0.04624694 5.155500e-02 9.204706e-02 1.203465e-01 1.525839e-01 2.285189e-01 2983.5996 0.9990648
## theta[226] 2.692910e-01 0.0006038929 0.03823546 1.997720e-01 2.419471e-01 2.683517e-01 2.936791e-01 3.513275e-01 4008.7856 0.9986002
## theta[227] 1.251501e-01 0.0009215863 0.04287868 5.274335e-02 9.335798e-02 1.214704e-01 1.515731e-01 2.182962e-01 2164.7651 0.9985410
## theta[228] 2.254173e-01 0.0002733773 0.01678433 1.938498e-01 2.136130e-01 2.252021e-01 2.367413e-01 2.597612e-01 3769.4938 0.9988345
## theta[229] 1.236102e-01 0.0007975827 0.04650171 4.372790e-02 9.148034e-02 1.193893e-01 1.501013e-01 2.297054e-01 3399.2753 0.9987750
## theta[230] 2.316515e-01 0.0003079494 0.01989398 1.955046e-01 2.179404e-01 2.308841e-01 2.444119e-01 2.719418e-01 4173.3514 0.9983751
## theta[231] 1.346564e-01 0.0007630768 0.04169534 6.089032e-02 1.048930e-01 1.313671e-01 1.621874e-01 2.202171e-01 2985.6469 0.9994136
## theta[232] 2.844244e-01 0.0002720028 0.01662979 2.521405e-01 2.731552e-01 2.842379e-01 2.957228e-01 3.164277e-01 3737.8899 0.9988323
## theta[233] 2.446600e-01 0.0003532266 0.02241169 2.018604e-01 2.305615e-01 2.441971e-01 2.589749e-01 2.897057e-01 4025.7098 0.9984192
## theta[234] 2.480223e-01 0.0002312184 0.01528158 2.195569e-01 2.370712e-01 2.475901e-01 2.582236e-01 2.778608e-01 4368.0894 0.9988140
## theta[235] 2.135884e-01 0.0004409564 0.02719383 1.637270e-01 1.944166e-01 2.127010e-01 2.315708e-01 2.687393e-01 3803.2019 0.9983020
## theta[236] 2.336576e-01 0.0005478333 0.03223092 1.742285e-01 2.117928e-01 2.327225e-01 2.542407e-01 2.983682e-01 3461.3743 1.0004214
## theta[237] 2.262361e-01 0.0004931794 0.02825372 1.748323e-01 2.058948e-01 2.256849e-01 2.452992e-01 2.836661e-01 3282.0216 0.9983594
## theta[238] 2.542243e-01 0.0005240815 0.02900692 1.990491e-01 2.343548e-01 2.532390e-01 2.724170e-01 3.140860e-01 3063.4129 0.9983938
## theta[239] 2.742704e-01 0.0006938150 0.03833996 2.017758e-01 2.489743e-01 2.722504e-01 2.971038e-01 3.524205e-01 3053.6276 0.9990634
## theta[240] 2.285643e-01 0.0004593845 0.02936513 1.728344e-01 2.080285e-01 2.275242e-01 2.482980e-01 2.863831e-01 4086.1192 0.9983120
## theta[241] 2.523481e-01 0.0002679886 0.01767241 2.178240e-01 2.402193e-01 2.518177e-01 2.641368e-01 2.885701e-01 4348.6971 0.9988285
## theta[242] 2.663600e-01 0.0005299609 0.03239626 2.080509e-01 2.439457e-01 2.643305e-01 2.886815e-01 3.280024e-01 3736.8191 0.9984949
## theta[243] 2.783232e-01 0.0004456998 0.02793850 2.259630e-01 2.591903e-01 2.772427e-01 2.973425e-01 3.339201e-01 3929.3546 0.9986980
## theta[244] 2.624065e-01 0.0002889194 0.01800844 2.282124e-01 2.501554e-01 2.618859e-01 2.749365e-01 2.976079e-01 3885.0717 0.9981800
## theta[245] 2.881574e-01 0.0002706088 0.01867816 2.530995e-01 2.755483e-01 2.876422e-01 3.006839e-01 3.253281e-01 4764.1369 0.9987720
## theta[246] 1.480336e-01 0.0008309368 0.04973489 6.613425e-02 1.107557e-01 1.425960e-01 1.794417e-01 2.621564e-01 3582.5014 0.9988910
## theta[247] 1.244557e-01 0.0006857055 0.04622319 4.786850e-02 9.110443e-02 1.196348e-01 1.530461e-01 2.294971e-01 4544.0653 0.9994842
## theta[248] 2.479878e-01 0.0005395761 0.03464999 1.836100e-01 2.251033e-01 2.473760e-01 2.707526e-01 3.148900e-01 4123.8308 0.9996240
## theta[249] 2.936128e-01 0.0002985911 0.01854923 2.567514e-01 2.808184e-01 2.931779e-01 3.059099e-01 3.306633e-01 3859.2059 0.9989226
## theta[250] 3.017622e-01 0.0003171191 0.02184858 2.605943e-01 2.855503e-01 3.016723e-01 3.170414e-01 3.454332e-01 4746.8071 0.9993080
## theta[251] 1.181808e-01 0.0008858181 0.04481728 4.829008e-02 8.535570e-02 1.148329e-01 1.439733e-01 2.172586e-01 2559.7750 0.9984625
## theta[252] 2.497680e-01 0.0003878544 0.02465510 2.011802e-01 2.326563e-01 2.502951e-01 2.663092e-01 2.987213e-01 4040.8800 0.9983642
## theta[253] 2.986474e-01 0.0002523945 0.01709521 2.654511e-01 2.875974e-01 2.979144e-01 3.098844e-01 3.326065e-01 4587.6364 0.9985516
## theta[254] 2.559757e-01 0.0002609911 0.01767648 2.213262e-01 2.441531e-01 2.559189e-01 2.679580e-01 2.907694e-01 4587.1235 0.9988406
## theta[255] 2.316687e-01 0.0004045611 0.02206997 1.894905e-01 2.166104e-01 2.310964e-01 2.464617e-01 2.754175e-01 2976.0168 0.9985977
## theta[256] 2.641904e-01 0.0002572822 0.01683059 2.313483e-01 2.528009e-01 2.641387e-01 2.749796e-01 2.974048e-01 4279.3653 0.9986894
## theta[257] 2.792644e-01 0.0003012605 0.01895240 2.425866e-01 2.663958e-01 2.789981e-01 2.916333e-01 3.162446e-01 3957.7105 0.9985378
## theta[258] 2.646988e-01 0.0007320648 0.04559447 1.845290e-01 2.327826e-01 2.622507e-01 2.955918e-01 3.553050e-01 3879.0497 0.9994289
## theta[259] 1.240072e-01 0.0006795647 0.04690541 4.779982e-02 8.998593e-02 1.186379e-01 1.500288e-01 2.310397e-01 4764.1369 0.9984301
## theta[260] 3.079300e-01 0.0002590163 0.01635433 2.768699e-01 2.972908e-01 3.080441e-01 3.188257e-01 3.400970e-01 3986.6817 0.9984315
## theta[261] 1.547769e-01 0.0009013121 0.04936869 7.396478e-02 1.196111e-01 1.487967e-01 1.845439e-01 2.659234e-01 3000.2183 0.9982451
## theta[262] 2.130633e-01 0.0003867491 0.02384383 1.675967e-01 1.966371e-01 2.118740e-01 2.288199e-01 2.624733e-01 3800.9617 0.9984344
## theta[263] 2.458193e-01 0.0002555398 0.01675593 2.142905e-01 2.346384e-01 2.455553e-01 2.567732e-01 2.800725e-01 4299.5163 0.9984939
## theta[264] 2.212925e-01 0.0004836108 0.02571810 1.716143e-01 2.035807e-01 2.201628e-01 2.387307e-01 2.752106e-01 2828.0428 0.9986693
## theta[265] 2.558385e-01 0.0003474754 0.02398370 2.098678e-01 2.403702e-01 2.553219e-01 2.705130e-01 3.049689e-01 4764.1369 0.9983087
## theta[266] 2.918827e-01 0.0002962219 0.02044605 2.527965e-01 2.783433e-01 2.917914e-01 3.053869e-01 3.328684e-01 4764.1369 0.9986896
## theta[267] 2.568330e-01 0.0007851631 0.04399653 1.783691e-01 2.251861e-01 2.562876e-01 2.877068e-01 3.459898e-01 3139.9088 0.9996961
## theta[268] 1.344141e-01 0.0006707263 0.03902185 7.012047e-02 1.054729e-01 1.304352e-01 1.592347e-01 2.158216e-01 3384.7385 0.9985751
## theta[269] 2.625180e-01 0.0006414685 0.03715461 1.904635e-01 2.399973e-01 2.608205e-01 2.851851e-01 3.402280e-01 3354.8631 0.9985444
## theta[270] 2.823218e-01 0.0003905040 0.02393170 2.341310e-01 2.668562e-01 2.817189e-01 2.978217e-01 3.310367e-01 3755.7455 0.9983930
## theta[271] 2.439418e-01 0.0004162271 0.02491231 1.956969e-01 2.264540e-01 2.428865e-01 2.607381e-01 2.937640e-01 3582.3428 0.9996557
## theta[272] 2.202179e-01 0.0004934499 0.02827189 1.687421e-01 1.995942e-01 2.195585e-01 2.393927e-01 2.754044e-01 3282.6437 0.9990600
## theta[273] 2.332985e-01 0.0004441783 0.02983522 1.775440e-01 2.129813e-01 2.327338e-01 2.528280e-01 2.943918e-01 4511.7389 0.9986788
## theta[274] 2.833135e-01 0.0003850695 0.02340251 2.394757e-01 2.675546e-01 2.830084e-01 2.986371e-01 3.310726e-01 3693.5737 0.9985901
## theta[275] 1.203792e-01 0.0007065806 0.04412995 4.867561e-02 8.872624e-02 1.154788e-01 1.488881e-01 2.161834e-01 3900.7089 0.9983909
## theta[276] 2.138440e-01 0.0005086127 0.02956767 1.602241e-01 1.938500e-01 2.126879e-01 2.322918e-01 2.756891e-01 3379.5580 0.9981061
## theta[277] 1.213080e-01 0.0008301530 0.04645565 4.382221e-02 8.975614e-02 1.158666e-01 1.472914e-01 2.348639e-01 3131.5605 0.9998793
## theta[278] 1.632950e-01 0.0008800500 0.04164623 9.417853e-02 1.335183e-01 1.586335e-01 1.905167e-01 2.537055e-01 2239.4259 0.9996833
## theta[279] 1.232226e-01 0.0007747873 0.04604919 4.745991e-02 9.017968e-02 1.184018e-01 1.504805e-01 2.315483e-01 3532.4739 0.9986877
## theta[280] 2.196908e-01 0.0002634923 0.01654553 1.892538e-01 2.084121e-01 2.192361e-01 2.305752e-01 2.525206e-01 3942.9879 0.9990850
## theta[281] 2.495878e-01 0.0004275308 0.02902423 1.941211e-01 2.297801e-01 2.487607e-01 2.682754e-01 3.078190e-01 4608.7875 0.9989002
## theta[282] 1.250384e-01 0.0008037874 0.04549247 4.882504e-02 9.248890e-02 1.205397e-01 1.520622e-01 2.266702e-01 3203.2922 0.9984409
## theta[283] 2.294730e-01 0.0002443408 0.01505403 2.019163e-01 2.184458e-01 2.287767e-01 2.406083e-01 2.589197e-01 3795.8911 0.9983387
## theta[284] 1.264623e-01 0.0007776220 0.04448403 5.362396e-02 9.403706e-02 1.216629e-01 1.538526e-01 2.261672e-01 3272.4363 0.9985756
## theta[285] 2.831210e-01 0.0002607014 0.01755114 2.516402e-01 2.710307e-01 2.824883e-01 2.944185e-01 3.176635e-01 4532.3584 0.9990930
## theta[286] 9.961996e-02 0.0006538863 0.02905489 5.206956e-02 7.797482e-02 9.696323e-02 1.187336e-01 1.609705e-01 1974.3943 0.9998010
## theta[287] 2.310344e-01 0.0004018855 0.02676054 1.799081e-01 2.126117e-01 2.310352e-01 2.481271e-01 2.874477e-01 4433.8906 0.9991074
## theta[288] 2.704028e-01 0.0006376602 0.03471802 2.059502e-01 2.463315e-01 2.708005e-01 2.941692e-01 3.407965e-01 2964.3614 0.9995057
## theta[289] 1.251388e-01 0.0007729199 0.04621324 4.902304e-02 9.138008e-02 1.197213e-01 1.540767e-01 2.225963e-01 3574.8998 0.9990555
## theta[290] 2.765458e-01 0.0002919890 0.01859577 2.405975e-01 2.637697e-01 2.765345e-01 2.895173e-01 3.130862e-01 4055.9778 0.9988960
## theta[291] 1.796213e-01 0.0007716817 0.03664776 1.134722e-01 1.529838e-01 1.780874e-01 2.043613e-01 2.567100e-01 2255.3731 0.9999636
## theta[292] 2.462364e-01 0.0006212238 0.03700814 1.761298e-01 2.205095e-01 2.461800e-01 2.694206e-01 3.207796e-01 3548.9370 0.9989084
## theta[293] 2.218360e-01 0.0007282118 0.04413847 1.409265e-01 1.929019e-01 2.205142e-01 2.504647e-01 3.140571e-01 3673.8303 0.9983750
## theta[294] 2.510997e-01 0.0003902779 0.02557420 2.047906e-01 2.323267e-01 2.511291e-01 2.680583e-01 3.022003e-01 4293.9420 0.9982058
## theta[295] 2.427307e-01 0.0003130037 0.02160437 2.008738e-01 2.281148e-01 2.422226e-01 2.570943e-01 2.854526e-01 4764.1369 0.9983531
## theta[296] 1.250630e-01 0.0007946591 0.04483311 4.978819e-02 9.335322e-02 1.216651e-01 1.515838e-01 2.275309e-01 3182.9951 0.9983475
## theta[297] 2.817209e-01 0.0002568259 0.01625196 2.517783e-01 2.708305e-01 2.813533e-01 2.926370e-01 3.138878e-01 4004.3666 0.9992631
## theta[298] 2.591732e-01 0.0003582594 0.02393853 2.133924e-01 2.427761e-01 2.577272e-01 2.758664e-01 3.073414e-01 4464.7774 0.9986346
## theta[299] 2.276229e-01 0.0003882815 0.02680024 1.764666e-01 2.086825e-01 2.267341e-01 2.457484e-01 2.810097e-01 4764.1369 0.9982040
## theta[300] 2.181175e-01 0.0004176060 0.02614945 1.681026e-01 2.011503e-01 2.169300e-01 2.342530e-01 2.740131e-01 3920.9549 0.9998549
## theta[301] 2.743980e-01 0.0003590048 0.02477949 2.252680e-01 2.586895e-01 2.737998e-01 2.900352e-01 3.242384e-01 4764.1369 0.9991941
## theta[302] 2.383872e-01 0.0006430755 0.04109586 1.640385e-01 2.097107e-01 2.368891e-01 2.649108e-01 3.217881e-01 4083.8731 0.9988496
## theta[303] 2.485984e-01 0.0007483570 0.04300370 1.672526e-01 2.202331e-01 2.466959e-01 2.754451e-01 3.381228e-01 3302.1287 0.9985507
## theta[304] 1.233937e-01 0.0007391056 0.04464603 5.003201e-02 9.122120e-02 1.190703e-01 1.480738e-01 2.252258e-01 3648.8221 0.9984467
## theta[305] 2.236817e-01 0.0005039920 0.02813750 1.716131e-01 2.053693e-01 2.219869e-01 2.406022e-01 2.804417e-01 3116.9064 0.9988548
## theta[306] 2.349106e-01 0.0002510202 0.01732610 2.021697e-01 2.227586e-01 2.346208e-01 2.467594e-01 2.697117e-01 4764.1369 0.9993442
## theta[307] 2.032524e-01 0.0005245302 0.02922103 1.479398e-01 1.827334e-01 2.025504e-01 2.227510e-01 2.617546e-01 3103.4877 0.9987361
## theta[308] 1.709712e-01 0.0007815273 0.04285183 9.696372e-02 1.391080e-01 1.671206e-01 1.990497e-01 2.617278e-01 3006.4254 0.9985077
## theta[309] 2.374707e-01 0.0003779525 0.02227086 1.945924e-01 2.214878e-01 2.368036e-01 2.533448e-01 2.819499e-01 3472.1591 0.9988239
## theta[310] 2.843037e-01 0.0002537660 0.01751562 2.492623e-01 2.723794e-01 2.841667e-01 2.962624e-01 3.198849e-01 4764.1369 0.9984109
## theta[311] 1.192266e-01 0.0005869656 0.03358923 6.206451e-02 9.473106e-02 1.162787e-01 1.404225e-01 1.903499e-01 3274.7247 0.9988385
## theta[312] 2.426158e-01 0.0005921022 0.03414701 1.787596e-01 2.176365e-01 2.418301e-01 2.655612e-01 3.138506e-01 3325.9209 0.9984567
## theta[313] 2.450843e-01 0.0004700711 0.02754039 1.951937e-01 2.256262e-01 2.436629e-01 2.640423e-01 3.012357e-01 3432.5206 0.9984376
## theta[314] 1.161084e-01 0.0007284846 0.04255858 4.572190e-02 8.597402e-02 1.113887e-01 1.422878e-01 2.104570e-01 3412.9778 0.9989878
## theta[315] 1.390863e-01 0.0007268825 0.04823375 5.799017e-02 1.044671e-01 1.343365e-01 1.692842e-01 2.496736e-01 4403.2544 0.9982331
## theta[316] 2.520779e-01 0.0007424632 0.04448653 1.693938e-01 2.216033e-01 2.498448e-01 2.815788e-01 3.407332e-01 3590.1056 0.9986000
## theta[317] 2.800892e-01 0.0003158168 0.02179854 2.389172e-01 2.656760e-01 2.798525e-01 2.946447e-01 3.234746e-01 4764.1369 0.9981121
## theta[318] 2.464224e-01 0.0003445793 0.01978387 2.071577e-01 2.331347e-01 2.461600e-01 2.595551e-01 2.873081e-01 3296.4333 0.9982401
## theta[319] 2.604590e-01 0.0003996862 0.02758743 2.090139e-01 2.422333e-01 2.602565e-01 2.774882e-01 3.173026e-01 4764.1369 0.9985086
## theta[320] 1.289571e-01 0.0007885578 0.04509701 5.338734e-02 9.468536e-02 1.258290e-01 1.572175e-01 2.277578e-01 3270.6081 0.9986437
## theta[321] 1.418331e-01 0.0008242075 0.04555558 6.539812e-02 1.092757e-01 1.384093e-01 1.689363e-01 2.441803e-01 3054.9921 0.9988787
## theta[322] 1.322271e-01 0.0007714008 0.04319158 5.971059e-02 1.016666e-01 1.276408e-01 1.584059e-01 2.284878e-01 3135.0030 0.9987053
## theta[323] 2.428146e-01 0.0005277100 0.02934621 1.879608e-01 2.219061e-01 2.415991e-01 2.623117e-01 3.001785e-01 3092.5267 0.9989111
## theta[324] 1.234546e-01 0.0007473097 0.04068573 4.963796e-02 9.571804e-02 1.199504e-01 1.484947e-01 2.085941e-01 2964.0335 0.9985217
## theta[325] 1.246569e-01 0.0007426736 0.04481497 4.927710e-02 9.315934e-02 1.199009e-01 1.532394e-01 2.224000e-01 3641.2480 0.9987923
## theta[326] 2.349341e-01 0.0008069705 0.04531442 1.543108e-01 2.032863e-01 2.327159e-01 2.645117e-01 3.302016e-01 3153.2442 0.9989301
## theta[327] 1.233071e-01 0.0008496346 0.04579814 4.834483e-02 9.051934e-02 1.181784e-01 1.525727e-01 2.252965e-01 2905.5704 0.9992256
## theta[328] 2.383529e-01 0.0006857183 0.03895621 1.647488e-01 2.117872e-01 2.389526e-01 2.640553e-01 3.140219e-01 3227.4673 0.9985577
## theta[329] 2.587235e-01 0.0004013498 0.02770226 2.074950e-01 2.392445e-01 2.581953e-01 2.775119e-01 3.122235e-01 4764.1369 0.9987732
## theta[330] 1.436716e-01 0.0008645559 0.04893438 6.059808e-02 1.081923e-01 1.387260e-01 1.733175e-01 2.543628e-01 3203.6273 0.9992446
## theta[331] 2.579022e-01 0.0002506346 0.01729948 2.253483e-01 2.467063e-01 2.579730e-01 2.689704e-01 2.931877e-01 4764.1369 0.9992972
## theta[332] 2.339695e-01 0.0003795589 0.02456550 1.870070e-01 2.172634e-01 2.329975e-01 2.500871e-01 2.840964e-01 4188.8330 0.9983151
## theta[333] 2.275785e-01 0.0003445081 0.02149494 1.851035e-01 2.134623e-01 2.273638e-01 2.409767e-01 2.707164e-01 3892.9011 0.9990573
## theta[334] 2.702938e-01 0.0002926632 0.01814046 2.362846e-01 2.579866e-01 2.697574e-01 2.825126e-01 3.072895e-01 3842.0277 0.9987637
## theta[335] 1.234508e-01 0.0007844072 0.04429551 4.912242e-02 9.210944e-02 1.181904e-01 1.508718e-01 2.207379e-01 3188.8667 0.9982443
## theta[336] 1.290878e-01 0.0007446900 0.04377776 5.687657e-02 9.868622e-02 1.260748e-01 1.545131e-01 2.265493e-01 3455.8601 0.9988584
## theta[337] 2.298889e-01 0.0006099974 0.03731633 1.610409e-01 2.046896e-01 2.285501e-01 2.547103e-01 3.037026e-01 3742.3287 0.9980822
## theta[338] 1.255424e-01 0.0008280496 0.04569508 4.950661e-02 9.191110e-02 1.210383e-01 1.540856e-01 2.236592e-01 3045.2730 1.0000639
## theta[339] 2.192206e-01 0.0004986521 0.02486384 1.710670e-01 2.024597e-01 2.181340e-01 2.348274e-01 2.713146e-01 2486.2288 0.9993719
## theta[340] 2.063443e-01 0.0003201584 0.01894455 1.714865e-01 1.927601e-01 2.061075e-01 2.188575e-01 2.437336e-01 3501.3740 0.9986853
## theta[341] 2.673851e-01 0.0004486338 0.02881034 2.138900e-01 2.467938e-01 2.666721e-01 2.867434e-01 3.272751e-01 4123.9437 0.9988409
## theta[342] 2.706198e-01 0.0003487626 0.02026590 2.319571e-01 2.568078e-01 2.700051e-01 2.846689e-01 3.112380e-01 3376.5412 1.0004181
## theta[343] 2.838888e-01 0.0003048100 0.01988459 2.458538e-01 2.703643e-01 2.837529e-01 2.973044e-01 3.223546e-01 4255.7381 0.9984180
## theta[344] 2.421751e-01 0.0005803616 0.03338586 1.794556e-01 2.182283e-01 2.414612e-01 2.646178e-01 3.083096e-01 3309.2367 0.9986513
## theta[345] 1.099088e-01 0.0005132241 0.02926957 5.859421e-02 8.940022e-02 1.076801e-01 1.283855e-01 1.751020e-01 3252.5086 1.0000019
## theta[346] 2.364756e-01 0.0002497027 0.01723516 2.027872e-01 2.248415e-01 2.359268e-01 2.483578e-01 2.708529e-01 4764.1369 0.9985297
## theta[347] 2.154813e-01 0.0004620311 0.02672550 1.645558e-01 1.980901e-01 2.146978e-01 2.323960e-01 2.699424e-01 3345.8720 0.9993882
## theta[348] 1.250424e-01 0.0008232891 0.04537043 4.935528e-02 9.324676e-02 1.204589e-01 1.516006e-01 2.310045e-01 3036.9734 0.9989750
## theta[349] 2.780504e-01 0.0003523301 0.02300444 2.334926e-01 2.626802e-01 2.772385e-01 2.924307e-01 3.267671e-01 4263.0832 0.9988043
## theta[350] 2.462750e-01 0.0003263482 0.01840749 2.119283e-01 2.346287e-01 2.454405e-01 2.580377e-01 2.832094e-01 3181.4611 0.9985457
## theta[351] 1.365198e-01 0.0006891470 0.03836814 6.896369e-02 1.089705e-01 1.338545e-01 1.623364e-01 2.195988e-01 3099.6853 0.9986984
## theta[352] 2.328350e-01 0.0007959674 0.04590028 1.509001e-01 2.004078e-01 2.300743e-01 2.641047e-01 3.271942e-01 3325.3704 0.9994599
## theta[353] 2.255327e-01 0.0007648581 0.03952436 1.524604e-01 1.992846e-01 2.236458e-01 2.499534e-01 3.081013e-01 2670.3485 0.9983580
## theta[354] 2.571735e-01 0.0002526529 0.01723240 2.242015e-01 2.450315e-01 2.570959e-01 2.687696e-01 2.918292e-01 4652.0357 0.9986236
## theta[355] 2.669766e-01 0.0007943842 0.04646487 1.796068e-01 2.352315e-01 2.643073e-01 2.969691e-01 3.613755e-01 3421.2767 0.9984317
## theta[356] 2.388670e-01 0.0005473561 0.03366509 1.746205e-01 2.158015e-01 2.382821e-01 2.591801e-01 3.114186e-01 3782.8539 0.9982635
## theta[357] 1.524763e-01 0.0009031377 0.04601557 7.891044e-02 1.198616e-01 1.492962e-01 1.800479e-01 2.527554e-01 2595.9818 0.9990692
## theta[358] 2.689116e-01 0.0004626766 0.02611916 2.213689e-01 2.509732e-01 2.678136e-01 2.863743e-01 3.225220e-01 3186.8632 0.9984921
## theta[359] 1.266458e-01 0.0007377675 0.04504144 5.208518e-02 9.349339e-02 1.217780e-01 1.540633e-01 2.201402e-01 3727.2243 1.0004414
## theta[360] 2.181585e-01 0.0005413158 0.03275633 1.591499e-01 1.938896e-01 2.166088e-01 2.405250e-01 2.842217e-01 3661.7531 0.9990591
## theta[361] 2.569591e-01 0.0007592650 0.04454815 1.757267e-01 2.263496e-01 2.550895e-01 2.843330e-01 3.526881e-01 3442.4890 0.9982607
## theta[362] 1.995202e-01 0.0004828647 0.02981308 1.448277e-01 1.788371e-01 1.979926e-01 2.189628e-01 2.611480e-01 3812.0871 0.9990974
## theta[363] 1.238500e-01 0.0007980349 0.04537346 4.705683e-02 9.462212e-02 1.187549e-01 1.489093e-01 2.340843e-01 3232.6600 1.0003104
## theta[364] 1.215749e-01 0.0005257460 0.03070086 6.832249e-02 9.879889e-02 1.190715e-01 1.422711e-01 1.852253e-01 3409.9582 0.9993703
## theta[365] 2.818504e-01 0.0002648344 0.01805549 2.478887e-01 2.692877e-01 2.813649e-01 2.950929e-01 3.161889e-01 4648.0413 0.9982106
## theta[366] 2.354210e-01 0.0004168003 0.02780470 1.825596e-01 2.166606e-01 2.351758e-01 2.524401e-01 2.937387e-01 4450.2090 0.9988423
## theta[367] 2.532640e-01 0.0002522422 0.01579488 2.237349e-01 2.422831e-01 2.532744e-01 2.632912e-01 2.853062e-01 3921.0019 0.9984590
## theta[368] 2.859385e-01 0.0002741355 0.01805804 2.514032e-01 2.735652e-01 2.856991e-01 2.984115e-01 3.210923e-01 4339.2085 0.9984159
## theta[369] 1.035292e-01 0.0005068821 0.03141773 4.916913e-02 8.193384e-02 1.001213e-01 1.232211e-01 1.698150e-01 3841.8088 0.9984066
## theta[370] 2.554438e-01 0.0002325826 0.01605349 2.247862e-01 2.442388e-01 2.550734e-01 2.667122e-01 2.872827e-01 4764.1369 0.9982795
## theta[371] 2.207253e-01 0.0004232990 0.02534414 1.706693e-01 2.036000e-01 2.202237e-01 2.378301e-01 2.713990e-01 3584.7632 0.9987149
## theta[372] 2.786218e-01 0.0002499528 0.01693601 2.448911e-01 2.673268e-01 2.788147e-01 2.894787e-01 3.125464e-01 4590.9884 0.9985294
## theta[373] 2.910017e-01 0.0006270107 0.03531219 2.278234e-01 2.659888e-01 2.906472e-01 3.127252e-01 3.642848e-01 3171.7536 0.9988917
## theta[374] 2.413245e-01 0.0005936041 0.03687645 1.701268e-01 2.158145e-01 2.405613e-01 2.663812e-01 3.121278e-01 3859.2624 0.9989817
## theta[375] 1.315771e-01 0.0007130451 0.04352995 5.836260e-02 1.015268e-01 1.268555e-01 1.573062e-01 2.334870e-01 3726.8535 1.0000157
## theta[376] 2.462374e-01 0.0003509332 0.02223621 2.028771e-01 2.307096e-01 2.461337e-01 2.617410e-01 2.893482e-01 4014.8817 0.9992534
## theta[377] 1.005087e-01 0.0007458265 0.03393982 4.381331e-02 7.559020e-02 9.797443e-02 1.221524e-01 1.707078e-01 2070.8254 0.9992959
## theta[378] 2.681868e-01 0.0003597099 0.02241327 2.260995e-01 2.526660e-01 2.675593e-01 2.827339e-01 3.111526e-01 3882.4464 0.9988027
## theta[379] 1.814096e-01 0.0007225798 0.04030562 1.114893e-01 1.537581e-01 1.788322e-01 2.063336e-01 2.674290e-01 3111.4261 0.9985908
## theta[380] 1.182562e-01 0.0007826770 0.03933336 5.414109e-02 9.030460e-02 1.153438e-01 1.420821e-01 2.042097e-01 2525.5557 0.9988705
## theta[381] 1.232686e-01 0.0008122555 0.04428622 4.920314e-02 9.106307e-02 1.195091e-01 1.512106e-01 2.215762e-01 2972.7058 0.9994184
## theta[382] 2.208813e-01 0.0005717489 0.03268814 1.594311e-01 1.983042e-01 2.208966e-01 2.423131e-01 2.845261e-01 3268.6604 0.9992480
## theta[383] 1.167710e-01 0.0007506850 0.04120901 4.971539e-02 8.743185e-02 1.127839e-01 1.406355e-01 2.080383e-01 3013.4837 0.9985547
## theta[384] 1.251602e-01 0.0005054957 0.03204103 7.027622e-02 1.014131e-01 1.227831e-01 1.479480e-01 1.908352e-01 4017.7041 0.9981279
## theta[385] 2.446523e-01 0.0006922624 0.04097585 1.704769e-01 2.159792e-01 2.427488e-01 2.710299e-01 3.293504e-01 3503.5989 0.9998461
## theta[386] 2.495477e-01 0.0002968691 0.01985396 2.118462e-01 2.360763e-01 2.492338e-01 2.636302e-01 2.875014e-01 4472.6431 0.9984171
## theta[387] 1.329198e-01 0.0004794792 0.03309496 7.585899e-02 1.088053e-01 1.303676e-01 1.546976e-01 2.032067e-01 4764.1369 0.9996919
## theta[388] 1.241696e-01 0.0007865949 0.04516571 4.819793e-02 9.260132e-02 1.205222e-01 1.512265e-01 2.231606e-01 3296.9738 1.0002406
## theta[389] 1.341171e-01 0.0008126092 0.04456892 5.856251e-02 1.036952e-01 1.303067e-01 1.617532e-01 2.318937e-01 3008.1593 0.9986064
## theta[390] 2.644883e-01 0.0002677520 0.01848097 2.293493e-01 2.516382e-01 2.635944e-01 2.769378e-01 3.013544e-01 4764.1369 0.9982268
## theta[391] 1.246016e-01 0.0007728416 0.04365536 5.194384e-02 9.286125e-02 1.199653e-01 1.513386e-01 2.260417e-01 3190.7599 0.9983711
## theta[392] 1.294700e-01 0.0007312450 0.04153985 5.870738e-02 9.954974e-02 1.267766e-01 1.544572e-01 2.194001e-01 3227.0383 0.9987013
## theta[393] 1.267595e-01 0.0008181680 0.04450041 5.088101e-02 9.588744e-02 1.217561e-01 1.529871e-01 2.299796e-01 2958.3054 0.9996276
## theta[394] 2.578142e-01 0.0003559013 0.02276405 2.144430e-01 2.418827e-01 2.578874e-01 2.730390e-01 3.026179e-01 4091.0965 0.9982458
## theta[395] 1.144488e-01 0.0007824469 0.04299585 4.582343e-02 8.158491e-02 1.102654e-01 1.437461e-01 2.032979e-01 3019.5583 0.9985519
## theta[396] 2.256842e-01 0.0003055894 0.01960099 1.890758e-01 2.115109e-01 2.252193e-01 2.397306e-01 2.651255e-01 4114.1439 0.9988979
## theta[397] 1.911429e-01 0.0006113407 0.03275451 1.313779e-01 1.683462e-01 1.901043e-01 2.136996e-01 2.580285e-01 2870.6184 0.9988377
## theta[398] 1.938723e-01 0.0003957005 0.02392881 1.487363e-01 1.779731e-01 1.934097e-01 2.098335e-01 2.418635e-01 3656.8653 0.9984986
## theta[399] 1.186769e-01 0.0007588143 0.04386344 4.505964e-02 8.705055e-02 1.153782e-01 1.453495e-01 2.129241e-01 3341.4461 0.9986835
## theta[400] 2.582303e-01 0.0005661259 0.03528568 1.939621e-01 2.335659e-01 2.562546e-01 2.830958e-01 3.281204e-01 3884.8198 0.9981006
## theta[401] 2.512418e-01 0.0004002825 0.02353449 2.087463e-01 2.352503e-01 2.500925e-01 2.664241e-01 2.996995e-01 3456.8186 0.9991245
## theta[402] 2.240968e-01 0.0004281768 0.02711751 1.743688e-01 2.052686e-01 2.233486e-01 2.422961e-01 2.817884e-01 4011.0080 0.9989351
## theta[403] 2.420472e-01 0.0004921186 0.03100128 1.824239e-01 2.208638e-01 2.419221e-01 2.620483e-01 3.059227e-01 3968.4401 0.9990143
## theta[404] 1.170467e-01 0.0007667152 0.04150613 5.007992e-02 8.614172e-02 1.118784e-01 1.441284e-01 2.099029e-01 2930.5987 0.9994857
## theta[405] 2.684300e-01 0.0002965536 0.01675227 2.362007e-01 2.573888e-01 2.677989e-01 2.796037e-01 3.017954e-01 3191.1039 0.9983108
## theta[406] 2.559553e-01 0.0002635699 0.01655761 2.241791e-01 2.445976e-01 2.553725e-01 2.669045e-01 2.889799e-01 3946.4253 1.0002262
## theta[407] 2.520668e-01 0.0003373407 0.01857066 2.162978e-01 2.399103e-01 2.514809e-01 2.634739e-01 2.899873e-01 3030.5225 0.9984316
## theta[408] 1.858032e-01 0.0010125002 0.04272097 1.112381e-01 1.560161e-01 1.814130e-01 2.124173e-01 2.822569e-01 1780.2946 0.9987120
## theta[409] 2.622844e-01 0.0006965227 0.04414228 1.761486e-01 2.326285e-01 2.618449e-01 2.916650e-01 3.481346e-01 4016.4175 0.9981734
## theta[410] 2.405498e-01 0.0006776632 0.04292875 1.615924e-01 2.117410e-01 2.386195e-01 2.686363e-01 3.308579e-01 4012.9952 0.9989287
## theta[411] 1.536082e-01 0.0008777060 0.04735244 7.385181e-02 1.210749e-01 1.497858e-01 1.807985e-01 2.630107e-01 2910.6271 0.9992848
## theta[412] 2.529777e-01 0.0002714600 0.01638744 2.214728e-01 2.421887e-01 2.524494e-01 2.635981e-01 2.860730e-01 3644.2683 0.9983805
## theta[413] 2.471987e-01 0.0004163559 0.02455437 2.010572e-01 2.298928e-01 2.467748e-01 2.640561e-01 2.955686e-01 3477.9879 0.9985800
## theta[414] 2.898659e-01 0.0003551259 0.02324571 2.470314e-01 2.725685e-01 2.895549e-01 3.058612e-01 3.358314e-01 4284.7057 0.9988350
## theta[415] 2.566340e-01 0.0004272187 0.02948780 2.038221e-01 2.356473e-01 2.558213e-01 2.756930e-01 3.166431e-01 4764.1369 0.9983938
## theta[416] 1.364090e-01 0.0007998140 0.04245038 6.443194e-02 1.066651e-01 1.323316e-01 1.612290e-01 2.309607e-01 2816.9892 0.9987891
## theta[417] 2.434607e-01 0.0003421763 0.02155228 2.040882e-01 2.280326e-01 2.430619e-01 2.582540e-01 2.862785e-01 3967.2222 0.9985740
## theta[418] 2.463416e-01 0.0004106745 0.02417782 2.010685e-01 2.294099e-01 2.461716e-01 2.623121e-01 2.931776e-01 3466.0821 0.9986463
## theta[419] 2.203377e-01 0.0005028109 0.03420639 1.545717e-01 1.980279e-01 2.190580e-01 2.419681e-01 2.890094e-01 4628.1259 0.9993653
## theta[420] 2.331490e-01 0.0006759082 0.03892852 1.608464e-01 2.060841e-01 2.317438e-01 2.599614e-01 3.090771e-01 3317.1141 0.9982526
## theta[421] 1.048645e-01 0.0007187500 0.03575733 4.597748e-02 7.954599e-02 1.013204e-01 1.269749e-01 1.841429e-01 2474.9955 0.9996979
## theta[422] 2.390647e-01 0.0002410496 0.01606672 2.085473e-01 2.281015e-01 2.387740e-01 2.499354e-01 2.714526e-01 4442.6442 0.9984294
## theta[423] 1.198067e-01 0.0006534057 0.03645406 5.984143e-02 9.243013e-02 1.163882e-01 1.431135e-01 1.966046e-01 3112.6186 0.9991349
## theta[424] 3.100475e-01 0.0003769356 0.02092524 2.698951e-01 2.953224e-01 3.093845e-01 3.247152e-01 3.505408e-01 3081.8158 0.9987085
## theta[425] 1.228010e-01 0.0007710876 0.04311486 5.385495e-02 9.067128e-02 1.184960e-01 1.501378e-01 2.150703e-01 3126.4143 0.9986489
## theta[426] 2.239755e-01 0.0004150426 0.02471454 1.786540e-01 2.059456e-01 2.234156e-01 2.416288e-01 2.727672e-01 3545.8448 0.9992069
## theta[427] 1.139652e-01 0.0005683313 0.03076034 5.995630e-02 9.070574e-02 1.122925e-01 1.343415e-01 1.769079e-01 2929.4040 0.9983826
## theta[428] 1.255053e-01 0.0007648947 0.04144275 5.561225e-02 9.603693e-02 1.210558e-01 1.513586e-01 2.142381e-01 2935.5796 0.9983713
## theta[429] 2.252366e-01 0.0002596365 0.01699768 1.927727e-01 2.137593e-01 2.251958e-01 2.360917e-01 2.600113e-01 4285.9599 0.9993942
## theta[430] 1.221464e-01 0.0008824431 0.04396242 5.030420e-02 9.134790e-02 1.173494e-01 1.486960e-01 2.244592e-01 2481.9311 0.9989750
## theta[431] 1.396264e-01 0.0008768212 0.04556614 6.213683e-02 1.067418e-01 1.363046e-01 1.674420e-01 2.408975e-01 2700.6135 0.9986218
## theta[432] 1.276055e-01 0.0008052543 0.04480239 5.064447e-02 9.589898e-02 1.233437e-01 1.539022e-01 2.263102e-01 3095.5390 0.9982956
## theta[433] 1.125073e-01 0.0006067478 0.03748220 5.039533e-02 8.542607e-02 1.092574e-01 1.363218e-01 1.954605e-01 3816.2224 0.9987800
## theta[434] 1.191451e-01 0.0006203573 0.03712751 5.202057e-02 9.359379e-02 1.168262e-01 1.417592e-01 1.976483e-01 3581.8532 0.9996886
## theta[435] 1.255828e-01 0.0007202412 0.04545664 5.021990e-02 9.344412e-02 1.222019e-01 1.512237e-01 2.335351e-01 3983.2610 0.9991454
## theta[436] 2.575080e-01 0.0006097493 0.04014189 1.836196e-01 2.303324e-01 2.572467e-01 2.836384e-01 3.364865e-01 4334.0414 0.9985798
## theta[437] 1.418804e-01 0.0008771416 0.04727965 6.183820e-02 1.089274e-01 1.364383e-01 1.674512e-01 2.521899e-01 2905.4212 0.9985991
## theta[438] 2.345912e-01 0.0006535111 0.03738779 1.631333e-01 2.106043e-01 2.339483e-01 2.577541e-01 3.140017e-01 3273.0578 0.9994690
## theta[439] 1.204732e-01 0.0007675373 0.04295738 4.995845e-02 8.908188e-02 1.161955e-01 1.462508e-01 2.141028e-01 3132.3957 1.0001683
## theta[440] 2.187454e-01 0.0003303223 0.02200521 1.779335e-01 2.024069e-01 2.181318e-01 2.340034e-01 2.632984e-01 4437.8763 0.9987284
## theta[441] 2.471094e-01 0.0003110781 0.02147146 2.054490e-01 2.324602e-01 2.462081e-01 2.609610e-01 2.905991e-01 4764.1369 0.9989510
## theta[442] 2.568336e-01 0.0002883832 0.01770292 2.226510e-01 2.449779e-01 2.570088e-01 2.689623e-01 2.908718e-01 3768.3367 0.9986750
## theta[443] 1.283624e-01 0.0008450090 0.04484307 5.266784e-02 9.603793e-02 1.231462e-01 1.585195e-01 2.271754e-01 2816.2290 0.9988468
## theta[444] 2.601261e-01 0.0007089029 0.03796207 1.860714e-01 2.349146e-01 2.582380e-01 2.830202e-01 3.412411e-01 2867.6513 0.9987493
## theta[445] 2.409565e-01 0.0002848021 0.01768125 2.076585e-01 2.286389e-01 2.406974e-01 2.530349e-01 2.754802e-01 3854.2483 0.9982754
## theta[446] 1.796880e-01 0.0009268878 0.04104470 1.068654e-01 1.526484e-01 1.762506e-01 2.049853e-01 2.671582e-01 1960.9200 0.9998884
## theta[447] 2.533180e-01 0.0004577171 0.02695371 2.036789e-01 2.342421e-01 2.536289e-01 2.718309e-01 3.060744e-01 3467.7100 0.9985580
## theta[448] 2.285687e-01 0.0005358747 0.03006751 1.723253e-01 2.073241e-01 2.277474e-01 2.485916e-01 2.889784e-01 3148.2444 0.9998867
## theta[449] 2.498845e-01 0.0002422181 0.01671855 2.178262e-01 2.387160e-01 2.493430e-01 2.603751e-01 2.832337e-01 4764.1369 0.9982763
## theta[450] 2.653714e-01 0.0003362874 0.02321147 2.192331e-01 2.490675e-01 2.652789e-01 2.809710e-01 3.118070e-01 4764.1369 0.9984953
## theta[451] 1.010155e-01 0.0005257453 0.02873680 5.170583e-02 8.085117e-02 9.863532e-02 1.179841e-01 1.659436e-01 2987.6258 0.9995429
## theta[452] 2.438481e-01 0.0006311843 0.04339095 1.606437e-01 2.143748e-01 2.420554e-01 2.720595e-01 3.348595e-01 4725.9148 0.9984553
## theta[453] 2.226417e-01 0.0003370527 0.02326430 1.821338e-01 2.068502e-01 2.213071e-01 2.381433e-01 2.701928e-01 4764.1369 0.9984927
## theta[454] 3.073412e-01 0.0002851015 0.01882136 2.709701e-01 2.942393e-01 3.067158e-01 3.204732e-01 3.462940e-01 4358.1591 0.9983097
## theta[455] 1.118104e-01 0.0005430800 0.03385245 5.241575e-02 8.812438e-02 1.092807e-01 1.336541e-01 1.842187e-01 3885.5515 0.9989402
## theta[456] 1.260045e-01 0.0007366893 0.04649207 4.804050e-02 9.352261e-02 1.211554e-01 1.531859e-01 2.335132e-01 3982.8058 0.9991242
## theta[457] 1.439426e-01 0.0007818821 0.04488690 6.911543e-02 1.112452e-01 1.385480e-01 1.727933e-01 2.435679e-01 3295.7688 0.9982359
## theta[458] 1.318288e-01 0.0009205338 0.04575721 5.238103e-02 1.018039e-01 1.274871e-01 1.584695e-01 2.330173e-01 2470.8118 1.0009248
## theta[459] 3.179119e-01 0.0003180912 0.02155318 2.772076e-01 3.028881e-01 3.179819e-01 3.330243e-01 3.609235e-01 4591.1283 0.9993436
## theta[460] 1.122150e-01 0.0006564499 0.03324446 5.449243e-02 8.864676e-02 1.097964e-01 1.334620e-01 1.814462e-01 2564.6931 0.9980444
## theta[461] 1.260301e-01 0.0009184388 0.04395660 5.296629e-02 9.415822e-02 1.223857e-01 1.522130e-01 2.272373e-01 2290.5923 0.9991344
## theta[462] 2.386987e-01 0.0003943421 0.02616010 1.895051e-01 2.201323e-01 2.378820e-01 2.566096e-01 2.922420e-01 4400.8100 0.9989526
## theta[463] 2.024981e-01 0.0003023535 0.01981549 1.661068e-01 1.890250e-01 2.018617e-01 2.161380e-01 2.413679e-01 4295.1611 0.9982437
## theta[464] 1.219745e-01 0.0008114773 0.04532576 4.497774e-02 9.075420e-02 1.172591e-01 1.486021e-01 2.247957e-01 3119.8764 0.9994095
## theta[465] 2.254340e-01 0.0004686643 0.03062300 1.685973e-01 2.052054e-01 2.244769e-01 2.445406e-01 2.886736e-01 4269.4472 0.9983625
## theta[466] 2.664935e-01 0.0003217223 0.02220615 2.251412e-01 2.511642e-01 2.655215e-01 2.818874e-01 3.098609e-01 4764.1369 0.9980232
## theta[467] 1.263649e-01 0.0007846466 0.04100629 5.777992e-02 9.699923e-02 1.231948e-01 1.511662e-01 2.161334e-01 2731.1955 0.9985746
## theta[468] 1.070668e-01 0.0005382581 0.02696865 5.968317e-02 8.730385e-02 1.051793e-01 1.249072e-01 1.636326e-01 2510.3679 0.9998717
## theta[469] 2.302720e-01 0.0004211013 0.02406008 1.838300e-01 2.140278e-01 2.292825e-01 2.467879e-01 2.779906e-01 3264.5327 0.9984388
## theta[470] 2.418334e-01 0.0004063597 0.02479734 1.958872e-01 2.241824e-01 2.412029e-01 2.595381e-01 2.902901e-01 3723.8224 0.9986806
## theta[471] 2.966346e-01 0.0002871918 0.01982276 2.600238e-01 2.820876e-01 2.966356e-01 3.102457e-01 3.359141e-01 4764.1369 0.9981421
## theta[472] 1.198844e-01 0.0006763905 0.04246336 4.571875e-02 8.972225e-02 1.163001e-01 1.456651e-01 2.118472e-01 3941.2471 0.9984551
## theta[473] 2.574849e-01 0.0003929421 0.02588175 2.084187e-01 2.402794e-01 2.567670e-01 2.731909e-01 3.108436e-01 4338.4044 0.9981368
## theta[474] 3.010907e-01 0.0003780101 0.02482287 2.533379e-01 2.845764e-01 3.007211e-01 3.172902e-01 3.511590e-01 4312.1820 0.9981837
## theta[475] 1.168518e-01 0.0008309916 0.04327200 4.723822e-02 8.629322e-02 1.128816e-01 1.426742e-01 2.161404e-01 2711.5693 0.9997111
## theta[476] 1.748506e-01 0.0007357506 0.03703762 1.112984e-01 1.485713e-01 1.725738e-01 1.984971e-01 2.536977e-01 2534.1064 0.9992749
## theta[477] 2.590855e-01 0.0003436061 0.02262305 2.156366e-01 2.435964e-01 2.588626e-01 2.741350e-01 3.068625e-01 4334.9173 0.9985843
## theta[478] 2.368440e-01 0.0005208053 0.03549373 1.733582e-01 2.113113e-01 2.355713e-01 2.605185e-01 3.066107e-01 4644.6460 0.9986908
## theta[479] 1.412572e-01 0.0007155649 0.03750671 7.554325e-02 1.159271e-01 1.388575e-01 1.637697e-01 2.200749e-01 2747.3863 0.9987238
## theta[480] 3.002061e-01 0.0002697089 0.01861605 2.630199e-01 2.874931e-01 2.999808e-01 3.124392e-01 3.381747e-01 4764.1369 0.9982349
## theta[481] 2.215896e-01 0.0003443858 0.02074320 1.830814e-01 2.071154e-01 2.212787e-01 2.349661e-01 2.649226e-01 3627.9477 0.9985563
## theta[482] 1.624399e-01 0.0006070187 0.03564091 9.484501e-02 1.383350e-01 1.601058e-01 1.843550e-01 2.390647e-01 3447.4131 0.9982407
## theta[483] 2.425420e-01 0.0003439367 0.02372803 1.980739e-01 2.258934e-01 2.416879e-01 2.592245e-01 2.904713e-01 4759.5531 0.9986578
## theta[484] 2.312944e-01 0.0006265135 0.03494602 1.655135e-01 2.066805e-01 2.297903e-01 2.550167e-01 3.032344e-01 3111.2473 0.9993260
## theta[485] 1.512874e-01 0.0007937451 0.04599738 7.185996e-02 1.194906e-01 1.470961e-01 1.793423e-01 2.525763e-01 3358.1808 0.9985235
## theta[486] 2.834645e-01 0.0002627364 0.01758298 2.511982e-01 2.712256e-01 2.830564e-01 2.959923e-01 3.178826e-01 4478.6248 0.9992674
## theta[487] 2.476481e-01 0.0005551923 0.03343758 1.846478e-01 2.253223e-01 2.460917e-01 2.706289e-01 3.146506e-01 3627.2951 1.0004254
## theta[488] 1.889528e-01 0.0005632819 0.03195192 1.297959e-01 1.670536e-01 1.884586e-01 2.105062e-01 2.538253e-01 3217.6759 0.9987735
## theta[489] 2.269532e-01 0.0004047930 0.02793992 1.731856e-01 2.084154e-01 2.258716e-01 2.452348e-01 2.837726e-01 4764.1369 0.9984234
## theta[490] 2.479950e-01 0.0003961517 0.02317461 2.030701e-01 2.324872e-01 2.471048e-01 2.631020e-01 2.940440e-01 3422.1700 1.0007042
## theta[491] 1.335224e-01 0.0007981075 0.04509312 6.024178e-02 1.008324e-01 1.303463e-01 1.611073e-01 2.325451e-01 3192.2563 0.9997954
## theta[492] 2.289155e-01 0.0003152740 0.02176107 1.860940e-01 2.141184e-01 2.282210e-01 2.441687e-01 2.720591e-01 4764.1369 0.9990099
## theta[493] 1.238319e-01 0.0007250567 0.04247577 5.148964e-02 9.496641e-02 1.193543e-01 1.493414e-01 2.151540e-01 3431.9318 0.9986484
## theta[494] 2.474237e-01 0.0003245213 0.02093565 2.079655e-01 2.336633e-01 2.473962e-01 2.612045e-01 2.884469e-01 4161.8503 0.9984813
## theta[495] 1.062397e-01 0.0006993052 0.03649590 4.480120e-02 7.917245e-02 1.027504e-01 1.299120e-01 1.833639e-01 2723.6703 0.9989500
## theta[496] 1.150518e-01 0.0007503573 0.03681707 5.307884e-02 8.938139e-02 1.119295e-01 1.369995e-01 1.932790e-01 2407.4772 1.0003361
## theta[497] 2.441474e-01 0.0003662600 0.02285871 2.007051e-01 2.284462e-01 2.444717e-01 2.596618e-01 2.907588e-01 3895.1534 0.9981113
## theta[498] 2.815465e-01 0.0002726075 0.01742763 2.489845e-01 2.691104e-01 2.813293e-01 2.936510e-01 3.171001e-01 4086.9645 0.9992963
## theta[499] 2.385324e-01 0.0004158019 0.02413724 1.928041e-01 2.215813e-01 2.380289e-01 2.542372e-01 2.874663e-01 3369.7867 0.9986891
## theta[500] 1.130001e-01 0.0004795328 0.03100670 6.019751e-02 9.033007e-02 1.106149e-01 1.331382e-01 1.810411e-01 4180.9442 0.9999392
## theta[501] 1.204221e-01 0.0006056562 0.04114027 5.187086e-02 9.093895e-02 1.158737e-01 1.463756e-01 2.088227e-01 4614.0451 0.9998185
## theta[502] 2.440696e-01 0.0002777781 0.01616729 2.122825e-01 2.326427e-01 2.444301e-01 2.547454e-01 2.756303e-01 3387.4945 0.9992179
## theta[503] 1.200191e-01 0.0007626967 0.04012171 5.798363e-02 9.115219e-02 1.151837e-01 1.443187e-01 2.078920e-01 2767.2937 0.9993461
## theta[504] 2.671877e-01 0.0003642770 0.02210107 2.268052e-01 2.520358e-01 2.667225e-01 2.812040e-01 3.136961e-01 3680.9755 0.9982684
## theta[505] 1.259329e-01 0.0009442444 0.04663041 5.058389e-02 9.149547e-02 1.190482e-01 1.565881e-01 2.244386e-01 2438.7629 0.9983711
## theta[506] 2.348531e-01 0.0003372240 0.02161884 1.925807e-01 2.205548e-01 2.343876e-01 2.490500e-01 2.770206e-01 4109.8669 0.9986511
## theta[507] 1.521665e-01 0.0008713611 0.04856264 7.379294e-02 1.188575e-01 1.468021e-01 1.798096e-01 2.572154e-01 3106.0489 0.9990375
## theta[508] 1.856610e-01 0.0004978723 0.02792583 1.318542e-01 1.672419e-01 1.848779e-01 2.034916e-01 2.428136e-01 3146.1272 0.9993734
## theta[509] 2.586297e-01 0.0002744403 0.01728779 2.237602e-01 2.472448e-01 2.586265e-01 2.701898e-01 2.925338e-01 3968.1033 1.0007248
## theta[510] 2.430968e-01 0.0004327412 0.02549201 1.964728e-01 2.247966e-01 2.428566e-01 2.592533e-01 2.957432e-01 3470.1795 0.9986104
## theta[511] 1.274857e-01 0.0005774396 0.03985646 5.833695e-02 9.829113e-02 1.252169e-01 1.535550e-01 2.157100e-01 4764.1369 0.9984138
## theta[512] 2.934930e-01 0.0003489452 0.01975126 2.562375e-01 2.794460e-01 2.931874e-01 3.077686e-01 3.310824e-01 3203.8724 0.9987741
## theta[513] 2.456593e-01 0.0003318298 0.02026697 2.073768e-01 2.320913e-01 2.452324e-01 2.585599e-01 2.884123e-01 3730.3261 0.9986373
## theta[514] 2.178681e-01 0.0004188665 0.02660159 1.679816e-01 2.003896e-01 2.175028e-01 2.350505e-01 2.729854e-01 4033.3311 0.9991035
## theta[515] 1.238276e-01 0.0007964400 0.04446887 5.103242e-02 9.172861e-02 1.199244e-01 1.499418e-01 2.246683e-01 3117.4975 0.9988382
## theta[516] 2.379292e-01 0.0007065336 0.04017643 1.565811e-01 2.101553e-01 2.377316e-01 2.650366e-01 3.160908e-01 3233.5319 1.0006968
## theta[517] 2.027957e-01 0.0005740830 0.03346885 1.396233e-01 1.799643e-01 2.005584e-01 2.243671e-01 2.740459e-01 3398.8521 0.9992991
## theta[518] 1.117309e-01 0.0006516033 0.03814396 4.804526e-02 8.532744e-02 1.080758e-01 1.344036e-01 1.973494e-01 3426.7709 0.9982662
## theta[519] 1.267748e-01 0.0008726362 0.04458253 5.338774e-02 9.499989e-02 1.224311e-01 1.525692e-01 2.239150e-01 2610.1348 0.9991512
## theta[520] 1.262341e-01 0.0007902650 0.04515177 5.109657e-02 9.450218e-02 1.218118e-01 1.511811e-01 2.283731e-01 3264.4051 0.9988844
## theta[521] 2.350707e-01 0.0003070192 0.02103681 1.942997e-01 2.201941e-01 2.355743e-01 2.490280e-01 2.766132e-01 4694.9265 0.9987822
## theta[522] 2.642487e-01 0.0002702767 0.01739309 2.310283e-01 2.524029e-01 2.635342e-01 2.759127e-01 3.000536e-01 4141.2937 0.9990775
## theta[523] 3.000719e-01 0.0003954088 0.02435816 2.533958e-01 2.829032e-01 2.995389e-01 3.158997e-01 3.487091e-01 3794.8665 0.9999009
## theta[524] 2.314781e-01 0.0006179068 0.03808510 1.588576e-01 2.060134e-01 2.298358e-01 2.555297e-01 3.102342e-01 3798.9553 0.9990439
## theta[525] 2.236337e-01 0.0002446870 0.01688897 1.920244e-01 2.125773e-01 2.232000e-01 2.338573e-01 2.579012e-01 4764.1369 0.9997304
## theta[526] 2.626999e-01 0.0004114645 0.02565808 2.131605e-01 2.456244e-01 2.625621e-01 2.800865e-01 3.147425e-01 3888.5134 0.9988620
## theta[527] 2.759530e-01 0.0002843351 0.01733434 2.418404e-01 2.640698e-01 2.749902e-01 2.873473e-01 3.099424e-01 3716.6652 0.9986502
## theta[528] 1.188408e-01 0.0007747156 0.04234593 5.072767e-02 8.694734e-02 1.153090e-01 1.456947e-01 2.130361e-01 2987.7121 0.9987084
## theta[529] 2.290571e-01 0.0002467313 0.01703007 1.962218e-01 2.182934e-01 2.290277e-01 2.401320e-01 2.633751e-01 4764.1369 0.9986080
## theta[530] 2.351119e-01 0.0003991233 0.02381178 1.911248e-01 2.181444e-01 2.343017e-01 2.511277e-01 2.837068e-01 3559.3426 0.9985574
## theta[531] 2.690869e-01 0.0002978602 0.01767754 2.351363e-01 2.573625e-01 2.688214e-01 2.805642e-01 3.036812e-01 3522.2357 0.9987575
## theta[532] 1.255127e-01 0.0008125139 0.04788668 4.493615e-02 9.046216e-02 1.202708e-01 1.545098e-01 2.320617e-01 3473.5041 0.9988427
## theta[533] 1.168408e-01 0.0005132078 0.03117890 6.230819e-02 9.500849e-02 1.145794e-01 1.373463e-01 1.839225e-01 3690.9235 0.9988215
## theta[534] 3.101432e-01 0.0004120153 0.02601135 2.622001e-01 2.922281e-01 3.097988e-01 3.265048e-01 3.633444e-01 3985.6501 0.9989844
## theta[535] 2.346348e-01 0.0007254707 0.04256084 1.542605e-01 2.045039e-01 2.324751e-01 2.625237e-01 3.218342e-01 3441.7603 0.9994837
## theta[536] 1.183876e-01 0.0008042507 0.04197276 4.701741e-02 8.783911e-02 1.163779e-01 1.446536e-01 2.072228e-01 2723.6552 0.9990922
## theta[537] 2.389633e-01 0.0003006231 0.01721775 2.052048e-01 2.276263e-01 2.384232e-01 2.502776e-01 2.732936e-01 3280.2608 0.9987342
## theta[538] 1.174809e-01 0.0007064318 0.03699010 5.423140e-02 9.111347e-02 1.152451e-01 1.399017e-01 2.000221e-01 2741.7669 0.9991620
## theta[539] 2.538547e-01 0.0003751412 0.02280355 2.113637e-01 2.379151e-01 2.540553e-01 2.687413e-01 3.003794e-01 3695.0081 0.9982762
## theta[540] 2.448761e-01 0.0005583296 0.03841835 1.711309e-01 2.199103e-01 2.437054e-01 2.693778e-01 3.236492e-01 4734.7394 0.9991047
## theta[541] 2.243369e-01 0.0007304501 0.04306810 1.423259e-01 1.955258e-01 2.243686e-01 2.520070e-01 3.110053e-01 3476.4049 0.9988699
## theta[542] 2.246965e-01 0.0005992731 0.03525776 1.569263e-01 2.015913e-01 2.236984e-01 2.463583e-01 2.961877e-01 3461.4634 0.9986087
## theta[543] 2.183264e-01 0.0006101497 0.03464169 1.524460e-01 1.953713e-01 2.179694e-01 2.398795e-01 2.893288e-01 3223.4818 0.9981953
## theta[544] 1.248628e-01 0.0006137652 0.03617287 6.576757e-02 9.847812e-02 1.214595e-01 1.472666e-01 2.044115e-01 3473.4528 0.9987982
## theta[545] 2.550120e-01 0.0009123571 0.04688238 1.677402e-01 2.224937e-01 2.524498e-01 2.853499e-01 3.537971e-01 2640.5213 0.9990142
## theta[546] 2.355401e-01 0.0002985006 0.02030936 1.959317e-01 2.217364e-01 2.349833e-01 2.490526e-01 2.778461e-01 4629.1571 0.9988978
## theta[547] 2.551491e-01 0.0007915789 0.04244501 1.741130e-01 2.273627e-01 2.534781e-01 2.824076e-01 3.413640e-01 2875.1791 0.9983686
## theta[548] 1.234832e-01 0.0008397844 0.04700549 4.603306e-02 8.874719e-02 1.192385e-01 1.509228e-01 2.345531e-01 3133.0078 0.9995891
## theta[549] 1.337097e-01 0.0005827521 0.03397755 7.551870e-02 1.106203e-01 1.319675e-01 1.538014e-01 2.066042e-01 3399.5107 0.9990437
## theta[550] 1.105039e-01 0.0005132514 0.02810852 6.193483e-02 9.002419e-02 1.090469e-01 1.282117e-01 1.695585e-01 2999.2710 0.9983091
## theta[551] 1.282042e-01 0.0008331094 0.04828276 4.750377e-02 9.356445e-02 1.239014e-01 1.551592e-01 2.411597e-01 3358.7687 0.9985538
## theta[552] 1.171700e-01 0.0008740030 0.04279213 4.743603e-02 8.728816e-02 1.128213e-01 1.421645e-01 2.125642e-01 2397.1877 0.9991530
## theta[553] 2.589714e-01 0.0002599830 0.01753630 2.279379e-01 2.464281e-01 2.585011e-01 2.713603e-01 2.926138e-01 4549.7375 0.9987822
## theta[554] 1.156872e-01 0.0007805649 0.04250903 4.357321e-02 8.534821e-02 1.121001e-01 1.407264e-01 2.125098e-01 2965.8165 0.9984529
## theta[555] 2.554168e-01 0.0005091089 0.03350784 1.907059e-01 2.321889e-01 2.543172e-01 2.779829e-01 3.217178e-01 4331.8305 0.9984828
## theta[556] 9.892602e-02 0.0006340320 0.02787686 5.054939e-02 7.850722e-02 9.711570e-02 1.169250e-01 1.581735e-01 1933.1493 0.9990507
## theta[557] 2.381016e-01 0.0007869497 0.04051552 1.629141e-01 2.110336e-01 2.376439e-01 2.632878e-01 3.224694e-01 2650.6288 0.9984611
## theta[558] 2.482144e-01 0.0004456910 0.02965951 1.923462e-01 2.278668e-01 2.472485e-01 2.685664e-01 3.081408e-01 4428.5374 0.9980740
## theta[559] 2.294289e-01 0.0005812581 0.03714302 1.601614e-01 2.024832e-01 2.293305e-01 2.533862e-01 3.045748e-01 4083.3466 0.9987358
## theta[560] 2.211596e-01 0.0005498366 0.03068237 1.647216e-01 2.002910e-01 2.204562e-01 2.421016e-01 2.839896e-01 3113.9426 0.9989419
## theta[561] 1.224712e-01 0.0007765199 0.04469758 4.979058e-02 8.939612e-02 1.175146e-01 1.515412e-01 2.216338e-01 3313.3159 0.9985558
## theta[562] 1.233833e-01 0.0007654803 0.04395445 5.104157e-02 9.097568e-02 1.202554e-01 1.515862e-01 2.200139e-01 3297.1425 1.0000969
## theta[563] 2.672440e-01 0.0003929657 0.02279453 2.255913e-01 2.512608e-01 2.668852e-01 2.833475e-01 3.122070e-01 3364.7443 0.9988866
## theta[564] 2.357756e-01 0.0003536741 0.02186166 1.948025e-01 2.200971e-01 2.355374e-01 2.505805e-01 2.797029e-01 3820.8470 0.9996759
## theta[565] 2.660205e-01 0.0006587640 0.04292940 1.850589e-01 2.367587e-01 2.652481e-01 2.930540e-01 3.526234e-01 4246.6846 0.9988374
## theta[566] 2.604000e-01 0.0004312164 0.02842861 2.086777e-01 2.407294e-01 2.595632e-01 2.788059e-01 3.188983e-01 4346.3117 0.9990437
## theta[567] 2.632184e-01 0.0004265942 0.02476382 2.178777e-01 2.460543e-01 2.630897e-01 2.799166e-01 3.135093e-01 3369.8108 0.9983955
## theta[568] 2.291347e-01 0.0003629928 0.02505475 1.821869e-01 2.119470e-01 2.281315e-01 2.466568e-01 2.796720e-01 4764.1369 0.9981549
## theta[569] 2.452546e-01 0.0002854399 0.01970184 2.080871e-01 2.312808e-01 2.447152e-01 2.589283e-01 2.835454e-01 4764.1369 0.9987289
## theta[570] 1.414579e-01 0.0004887720 0.03361470 8.372723e-02 1.175357e-01 1.390995e-01 1.619950e-01 2.156834e-01 4729.8330 0.9982277
## theta[571] 1.423970e-01 0.0008746011 0.04873124 5.966424e-02 1.099861e-01 1.370290e-01 1.697579e-01 2.594877e-01 3104.5232 0.9987235
## theta[572] 2.861345e-01 0.0003670166 0.02329883 2.419034e-01 2.707276e-01 2.851585e-01 3.013060e-01 3.328534e-01 4029.9240 0.9992862
## theta[573] 2.038598e-01 0.0007543195 0.03949915 1.270794e-01 1.778086e-01 2.023177e-01 2.294019e-01 2.841634e-01 2741.9836 0.9982251
## theta[574] 2.478008e-01 0.0007328085 0.04404995 1.676375e-01 2.173418e-01 2.473646e-01 2.763840e-01 3.388724e-01 3613.3476 0.9984453
## theta[575] 1.268800e-01 0.0008381963 0.04599210 4.978175e-02 9.443017e-02 1.225263e-01 1.539151e-01 2.314067e-01 3010.7520 0.9982782
## theta[576] 1.263468e-01 0.0008394657 0.04445403 5.083346e-02 9.321043e-02 1.226835e-01 1.543750e-01 2.260394e-01 2804.2472 0.9997239
## theta[577] 2.295919e-01 0.0003502172 0.02224744 1.874267e-01 2.138590e-01 2.294854e-01 2.450475e-01 2.754518e-01 4035.3843 0.9985258
## theta[578] 2.340125e-01 0.0007763408 0.04024968 1.585236e-01 2.069645e-01 2.331857e-01 2.602697e-01 3.202841e-01 2687.9421 0.9981667
## theta[579] 1.260908e-01 0.0007363327 0.04517580 5.115670e-02 9.513267e-02 1.206950e-01 1.517531e-01 2.339863e-01 3764.1215 0.9995514
## theta[580] 1.345786e-01 0.0007651687 0.04256094 6.273886e-02 1.033508e-01 1.314437e-01 1.611349e-01 2.283062e-01 3093.9126 0.9983452
## theta[581] 2.322976e-01 0.0006380041 0.03827980 1.643983e-01 2.071988e-01 2.306134e-01 2.572498e-01 3.140834e-01 3599.9170 0.9990640
## theta[582] 2.351499e-01 0.0003323149 0.01961401 1.975071e-01 2.215646e-01 2.351927e-01 2.486311e-01 2.720321e-01 3483.6395 0.9982122
## theta[583] 2.566876e-01 0.0005406503 0.02868333 2.034248e-01 2.377885e-01 2.555671e-01 2.753201e-01 3.151260e-01 2814.6615 0.9992009
## theta[584] 1.481785e-01 0.0004553291 0.03142806 9.061611e-02 1.260723e-01 1.466038e-01 1.678522e-01 2.149653e-01 4764.1369 0.9983699
## theta[585] 2.555511e-01 0.0003696099 0.02301196 2.117486e-01 2.392294e-01 2.553251e-01 2.714463e-01 3.016403e-01 3876.3243 0.9980996
## theta[586] 1.303349e-01 0.0008870367 0.04874262 4.965960e-02 9.503962e-02 1.261930e-01 1.600859e-01 2.353521e-01 3019.4972 0.9991280
## theta[587] 2.582899e-01 0.0004257524 0.02630385 2.093501e-01 2.394113e-01 2.582378e-01 2.756772e-01 3.108147e-01 3817.0203 0.9993721
## theta[588] 1.256910e-01 0.0007742008 0.04551467 5.011175e-02 9.409943e-02 1.194165e-01 1.534858e-01 2.281321e-01 3456.1731 0.9993061
## theta[589] 2.323694e-01 0.0009790832 0.04835937 1.459133e-01 1.993129e-01 2.297529e-01 2.630062e-01 3.348985e-01 2439.6192 0.9988031
## theta[590] 1.158441e-01 0.0005606046 0.03369341 5.913787e-02 9.247766e-02 1.125890e-01 1.378499e-01 1.888347e-01 3612.2402 0.9985310
## theta[591] 2.983353e-01 0.0002732277 0.01708205 2.674768e-01 2.865305e-01 2.983649e-01 3.099683e-01 3.304886e-01 3908.6856 0.9988595
## theta[592] 8.329258e-02 0.0005700800 0.02447205 4.122641e-02 6.642621e-02 8.087775e-02 9.823565e-02 1.353378e-01 1842.7614 0.9989414
## theta[593] 2.245938e-01 0.0005742584 0.03214955 1.623774e-01 2.017763e-01 2.231724e-01 2.468733e-01 2.886782e-01 3134.2594 0.9983239
## theta[594] 2.560760e-01 0.0002837338 0.01958408 2.186751e-01 2.431922e-01 2.558065e-01 2.684237e-01 2.947632e-01 4764.1369 0.9989046
## theta[595] 2.545991e-01 0.0004701733 0.02752441 2.032621e-01 2.358024e-01 2.536409e-01 2.717767e-01 3.107174e-01 3427.0467 0.9983376
## theta[596] 2.262934e-01 0.0002546043 0.01671390 1.942260e-01 2.143702e-01 2.263759e-01 2.382466e-01 2.581197e-01 4309.4725 0.9984211
## theta[597] 1.486834e-01 0.0007809106 0.04236198 7.450488e-02 1.189231e-01 1.453881e-01 1.723821e-01 2.485629e-01 2942.7256 0.9986452
## theta[598] 2.510664e-01 0.0002881148 0.01820805 2.158733e-01 2.385615e-01 2.504307e-01 2.632288e-01 2.874603e-01 3993.8878 0.9990032
## theta[599] 2.646521e-01 0.0002747709 0.01742474 2.314482e-01 2.531329e-01 2.643166e-01 2.759482e-01 2.992271e-01 4021.5298 0.9983561
## theta[600] 2.324006e-01 0.0004500503 0.02735769 1.797106e-01 2.139700e-01 2.324126e-01 2.513821e-01 2.857097e-01 3695.1885 0.9981547
## theta[601] 2.584190e-01 0.0003995394 0.02383896 2.139159e-01 2.424105e-01 2.576030e-01 2.748160e-01 3.076064e-01 3560.0442 0.9993166
## theta[602] 2.941075e-01 0.0002814960 0.01759225 2.588610e-01 2.828613e-01 2.939497e-01 3.055248e-01 3.287119e-01 3905.6960 0.9989435
## theta[603] 2.385695e-01 0.0003801447 0.02493382 1.907014e-01 2.217907e-01 2.385897e-01 2.545918e-01 2.876403e-01 4302.0936 0.9988419
## theta[604] 2.506838e-01 0.0005084987 0.03159291 1.911078e-01 2.291710e-01 2.492700e-01 2.722089e-01 3.164908e-01 3860.1096 0.9994616
## theta[605] 1.603539e-01 0.0005436927 0.03345000 1.032621e-01 1.360551e-01 1.580836e-01 1.826411e-01 2.318051e-01 3785.1696 0.9982885
## theta[606] 2.519691e-01 0.0005354222 0.03240333 1.932649e-01 2.287056e-01 2.517406e-01 2.737746e-01 3.146082e-01 3662.5764 0.9983788
## theta[607] 1.226286e-01 0.0007527897 0.04390282 4.937290e-02 9.153189e-02 1.178726e-01 1.501769e-01 2.185296e-01 3401.2414 0.9994124
## theta[608] 1.570795e-01 0.0005737100 0.03338599 9.612587e-02 1.327834e-01 1.547032e-01 1.788268e-01 2.259731e-01 3386.4430 0.9985432
## theta[609] 2.810708e-01 0.0003587838 0.02220631 2.386015e-01 2.653766e-01 2.805142e-01 2.958497e-01 3.265878e-01 3830.7786 0.9991832
## theta[610] 2.384270e-01 0.0006342193 0.03252052 1.756572e-01 2.165311e-01 2.377978e-01 2.598743e-01 3.027743e-01 2629.2753 1.0000963
## theta[611] 2.365910e-01 0.0004444112 0.02802946 1.841447e-01 2.169294e-01 2.357910e-01 2.564824e-01 2.934741e-01 3977.9508 0.9989832
## theta[612] 2.715561e-01 0.0005132307 0.03036738 2.126358e-01 2.510603e-01 2.711064e-01 2.906600e-01 3.331696e-01 3500.9784 0.9992757
## theta[613] 2.183995e-01 0.0004399699 0.02452070 1.721597e-01 2.015974e-01 2.174477e-01 2.349170e-01 2.668280e-01 3106.1319 1.0003718
## theta[614] 1.069440e-01 0.0006470346 0.03531515 4.609959e-02 8.129940e-02 1.038036e-01 1.296127e-01 1.814647e-01 2978.9766 0.9991797
## theta[615] 2.420469e-01 0.0006169175 0.03357652 1.747086e-01 2.203939e-01 2.409346e-01 2.635680e-01 3.090888e-01 2962.2188 0.9986153
## theta[616] 1.187344e-01 0.0008146171 0.04250764 4.958210e-02 8.754341e-02 1.137825e-01 1.450856e-01 2.120201e-01 2722.8703 0.9997397
## theta[617] 1.795964e-01 0.0009349164 0.04691465 9.707458e-02 1.480589e-01 1.763891e-01 2.087594e-01 2.874585e-01 2518.0903 0.9982634
## theta[618] 2.889996e-01 0.0002844578 0.01845773 2.523446e-01 2.763001e-01 2.890635e-01 3.011528e-01 3.259337e-01 4210.3776 0.9994464
## theta[619] 2.936094e-01 0.0003065521 0.02052142 2.552891e-01 2.798905e-01 2.936387e-01 3.059873e-01 3.364117e-01 4481.3234 0.9987738
## theta[620] 2.467326e-01 0.0005130691 0.03128095 1.890550e-01 2.256220e-01 2.460135e-01 2.674248e-01 3.116498e-01 3717.1322 0.9985437
## theta[621] 2.364551e-01 0.0005286938 0.03294076 1.737398e-01 2.138921e-01 2.353985e-01 2.573147e-01 3.048577e-01 3882.0292 0.9983144
## theta[622] 1.192702e-01 0.0006894374 0.04152002 5.147137e-02 8.848144e-02 1.162732e-01 1.454603e-01 2.078882e-01 3626.8146 0.9991634
## theta[623] 2.028727e-01 0.0005070171 0.02962432 1.491761e-01 1.818942e-01 2.019506e-01 2.218101e-01 2.634041e-01 3413.9065 0.9983333
## theta[624] 2.475787e-01 0.0002955237 0.01739111 2.146925e-01 2.360459e-01 2.466137e-01 2.592634e-01 2.820993e-01 3463.1400 0.9989650
## theta[625] 2.438661e-01 0.0002642019 0.01743999 2.115713e-01 2.315290e-01 2.439174e-01 2.561559e-01 2.779457e-01 4357.3327 0.9989589
## theta[626] 2.645417e-01 0.0005372255 0.03138974 2.050959e-01 2.433536e-01 2.626673e-01 2.847918e-01 3.308467e-01 3413.9907 0.9987843
## theta[627] 1.235044e-01 0.0007393092 0.04389881 5.049998e-02 9.177923e-02 1.190276e-01 1.509619e-01 2.237254e-01 3525.7647 0.9982261
## theta[628] 3.287545e-01 0.0003262865 0.01957750 2.919404e-01 3.152938e-01 3.285321e-01 3.418162e-01 3.672929e-01 3600.1138 1.0001479
## theta[629] 2.623873e-01 0.0008991839 0.04671710 1.743437e-01 2.310575e-01 2.617038e-01 2.925232e-01 3.585841e-01 2699.3222 0.9999154
## theta[630] 1.239803e-01 0.0007634590 0.04296952 5.108740e-02 9.258736e-02 1.210508e-01 1.494219e-01 2.207169e-01 3167.7392 1.0002346
## theta[631] 2.715862e-01 0.0002661142 0.01676615 2.403375e-01 2.600747e-01 2.709394e-01 2.828019e-01 3.046263e-01 3969.4523 0.9984931
## theta[632] 1.239556e-01 0.0007620073 0.04440559 5.319353e-02 9.016856e-02 1.193714e-01 1.511412e-01 2.205690e-01 3395.9161 0.9997146
## theta[633] 2.834274e-01 0.0003072614 0.01810774 2.483759e-01 2.709787e-01 2.832607e-01 2.951585e-01 3.198171e-01 3473.0589 0.9991190
## theta[634] 2.595381e-01 0.0003381370 0.01969216 2.209438e-01 2.466503e-01 2.594435e-01 2.720979e-01 2.980906e-01 3391.5749 0.9994054
## theta[635] 2.086785e-01 0.0004699841 0.02774477 1.549482e-01 1.889002e-01 2.081255e-01 2.280456e-01 2.650767e-01 3484.9438 0.9988758
## theta[636] 2.341264e-01 0.0003824227 0.02248823 1.918620e-01 2.184046e-01 2.335431e-01 2.493748e-01 2.770488e-01 3457.9863 0.9982567
## theta[637] 2.481522e-01 0.0003153186 0.01672763 2.161721e-01 2.372225e-01 2.476494e-01 2.591140e-01 2.819917e-01 2814.2971 1.0003353
## theta[638] 2.719059e-01 0.0002364777 0.01632234 2.396620e-01 2.607080e-01 2.714580e-01 2.826750e-01 3.038668e-01 4764.1369 0.9985197
## theta[639] 1.163879e-01 0.0007580868 0.04300873 4.497004e-02 8.503869e-02 1.116410e-01 1.436372e-01 2.163793e-01 3218.6624 0.9993301
## theta[640] 3.201004e-01 0.0003204961 0.01816316 2.849716e-01 3.085401e-01 3.195689e-01 3.316312e-01 3.563088e-01 3211.7172 0.9983961
## theta[641] 2.150129e-01 0.0003764500 0.02598361 1.665771e-01 1.970842e-01 2.148170e-01 2.325321e-01 2.661968e-01 4764.1369 0.9987134
## theta[642] 2.787532e-01 0.0003151359 0.01927116 2.414451e-01 2.657932e-01 2.786293e-01 2.911671e-01 3.173571e-01 3739.5549 0.9983562
## theta[643] 2.259838e-01 0.0003344626 0.02064041 1.870777e-01 2.114207e-01 2.253083e-01 2.391297e-01 2.682608e-01 3808.3892 0.9993081
## theta[644] 2.495722e-01 0.0002500028 0.01725587 2.154998e-01 2.375050e-01 2.492305e-01 2.617779e-01 2.838865e-01 4764.1369 0.9995250
## theta[645] 2.609353e-01 0.0004009375 0.02701095 2.111770e-01 2.436594e-01 2.598346e-01 2.782473e-01 3.151711e-01 4538.6468 0.9988277
## theta[646] 2.271745e-01 0.0004036991 0.02497436 1.787316e-01 2.097957e-01 2.273698e-01 2.431044e-01 2.757416e-01 3827.1302 0.9985271
## theta[647] 2.213836e-01 0.0007207388 0.03798654 1.521692e-01 1.960770e-01 2.194405e-01 2.470358e-01 2.992052e-01 2777.8169 1.0007131
## theta[648] 1.277060e-01 0.0008899278 0.04644223 4.926081e-02 9.496090e-02 1.234951e-01 1.549428e-01 2.290858e-01 2723.4326 0.9994573
## theta[649] 1.144525e-01 0.0006357282 0.03374847 5.708068e-02 9.005022e-02 1.111101e-01 1.342077e-01 1.884614e-01 2818.1580 0.9991351
## theta[650] 2.657921e-01 0.0005935403 0.03117184 2.087240e-01 2.443026e-01 2.649184e-01 2.853892e-01 3.276645e-01 2758.1914 1.0003530
## theta[651] 2.147308e-01 0.0010175137 0.03983033 1.412728e-01 1.871385e-01 2.129204e-01 2.410570e-01 2.959664e-01 1532.3125 0.9989722
## theta[652] 1.236396e-01 0.0007434466 0.04188907 5.063214e-02 9.244647e-02 1.195258e-01 1.510412e-01 2.145426e-01 3174.6942 0.9988697
## theta[653] 2.215301e-01 0.0006051047 0.03310264 1.615161e-01 1.984867e-01 2.206138e-01 2.426093e-01 2.922621e-01 2992.7082 0.9990384
## theta[654] 9.978610e-02 0.0005247037 0.02821881 5.085553e-02 8.003624e-02 9.700145e-02 1.179783e-01 1.623508e-01 2892.3396 0.9984505
## theta[655] 2.829242e-01 0.0002906067 0.01970491 2.449872e-01 2.691019e-01 2.829403e-01 2.964942e-01 3.207881e-01 4597.6659 0.9982869
## theta[656] 2.440129e-01 0.0002643123 0.01648575 2.115582e-01 2.327658e-01 2.440218e-01 2.550667e-01 2.761009e-01 3890.2954 0.9988490
## theta[657] 2.300801e-01 0.0002922859 0.02017437 1.929386e-01 2.153719e-01 2.296548e-01 2.449872e-01 2.678816e-01 4764.1369 0.9984096
## theta[658] 2.032531e-01 0.0004765811 0.02911632 1.504910e-01 1.829374e-01 2.023877e-01 2.236854e-01 2.613271e-01 3732.4949 0.9984061
## theta[659] 2.271626e-01 0.0006097970 0.03618166 1.580275e-01 2.027059e-01 2.259210e-01 2.507670e-01 3.008219e-01 3520.5167 0.9983848
## theta[660] 1.336880e-01 0.0007415326 0.04165065 6.021104e-02 1.056730e-01 1.307267e-01 1.577813e-01 2.256602e-01 3154.8821 0.9995715
## theta[661] 3.170481e-01 0.0002620699 0.01808878 2.829132e-01 3.045952e-01 3.164989e-01 3.288455e-01 3.539921e-01 4764.1369 0.9982125
## theta[662] 1.216889e-01 0.0008322362 0.04349698 5.240276e-02 8.931037e-02 1.163668e-01 1.492048e-01 2.188171e-01 2731.6502 0.9984809
## theta[663] 2.216813e-01 0.0005228253 0.03363514 1.579874e-01 1.990105e-01 2.207758e-01 2.440295e-01 2.904369e-01 4138.7882 0.9984935
## theta[664] 2.700877e-01 0.0003324406 0.02096553 2.309772e-01 2.563541e-01 2.692968e-01 2.845513e-01 3.114510e-01 3977.2573 0.9985065
## theta[665] 2.399761e-01 0.0004431979 0.02598110 1.915675e-01 2.222174e-01 2.393092e-01 2.564650e-01 2.920412e-01 3436.5265 0.9992305
## theta[666] 2.148179e-01 0.0005263608 0.03019112 1.571827e-01 1.938603e-01 2.133618e-01 2.348363e-01 2.747500e-01 3289.9658 1.0005623
## theta[667] 2.422134e-01 0.0003908743 0.02270611 2.007072e-01 2.253550e-01 2.416426e-01 2.578706e-01 2.870114e-01 3374.5151 0.9986213
## theta[668] 2.579304e-01 0.0004276486 0.02368707 2.142603e-01 2.410735e-01 2.578760e-01 2.740264e-01 3.040798e-01 3067.9519 0.9988474
## theta[669] 2.352738e-01 0.0008051079 0.04269557 1.539589e-01 2.053956e-01 2.338007e-01 2.635452e-01 3.206865e-01 2812.2735 0.9996870
## theta[670] 1.276027e-01 0.0008488225 0.04786762 5.093442e-02 9.317531e-02 1.225657e-01 1.561935e-01 2.339498e-01 3180.1666 0.9993431
## theta[671] 1.162339e-01 0.0007056564 0.03450867 5.384722e-02 9.227504e-02 1.137406e-01 1.379964e-01 1.891630e-01 2391.4978 0.9989900
## theta[672] 1.255909e-01 0.0007052871 0.04427011 5.418569e-02 9.363088e-02 1.220211e-01 1.528895e-01 2.190425e-01 3939.9378 0.9984011
## theta[673] 2.743820e-01 0.0002643211 0.01824416 2.385912e-01 2.622146e-01 2.742873e-01 2.865513e-01 3.116938e-01 4764.1369 0.9982529
## theta[674] 1.272343e-01 0.0009238782 0.04619360 4.977228e-02 9.345738e-02 1.219958e-01 1.586819e-01 2.315566e-01 2499.9662 0.9992544
## theta[675] 2.373911e-01 0.0007306312 0.03953984 1.617152e-01 2.092311e-01 2.369095e-01 2.635641e-01 3.165934e-01 2928.6890 1.0003387
## theta[676] 1.813891e-01 0.0003668421 0.02357705 1.377913e-01 1.653074e-01 1.804991e-01 1.964999e-01 2.301861e-01 4130.6718 0.9988074
## theta[677] 2.332738e-01 0.0004661335 0.02960822 1.780126e-01 2.123986e-01 2.322155e-01 2.533028e-01 2.914212e-01 4034.6320 0.9985117
## theta[678] 2.893460e-01 0.0003026279 0.01994443 2.509990e-01 2.766384e-01 2.891828e-01 3.019938e-01 3.290443e-01 4343.3546 0.9983042
## theta[679] 2.324699e-01 0.0004557991 0.02786471 1.804479e-01 2.142148e-01 2.320806e-01 2.507745e-01 2.889060e-01 3737.3354 0.9996943
## theta[680] 2.695067e-01 0.0002899459 0.01716846 2.368559e-01 2.581853e-01 2.688626e-01 2.803751e-01 3.038496e-01 3506.1374 0.9986240
## theta[681] 1.247704e-01 0.0008378815 0.04629442 4.895532e-02 9.060849e-02 1.202383e-01 1.530494e-01 2.233315e-01 3052.7555 0.9991032
## theta[682] 2.727763e-01 0.0005754051 0.03306718 2.083089e-01 2.493749e-01 2.718704e-01 2.944282e-01 3.398504e-01 3302.5317 0.9982438
## theta[683] 2.428904e-01 0.0003195469 0.02128213 2.012796e-01 2.284795e-01 2.428228e-01 2.571824e-01 2.865840e-01 4435.6869 0.9983075
## theta[684] 2.696614e-01 0.0002744100 0.01710302 2.374016e-01 2.580065e-01 2.694775e-01 2.813811e-01 3.036438e-01 3884.5928 0.9984970
## theta[685] 2.444253e-01 0.0004163178 0.02674103 1.950664e-01 2.250779e-01 2.443558e-01 2.625090e-01 2.981409e-01 4125.7811 0.9982745
## theta[686] 2.403283e-01 0.0004220166 0.02766828 1.859133e-01 2.215087e-01 2.398552e-01 2.585066e-01 2.947189e-01 4298.3849 0.9991964
## theta[687] 2.293180e-01 0.0007035664 0.04415570 1.459852e-01 1.991265e-01 2.288115e-01 2.558694e-01 3.218239e-01 3938.7962 0.9983779
## theta[688] 2.161673e-01 0.0003189534 0.02199491 1.764076e-01 2.002717e-01 2.154159e-01 2.310028e-01 2.602396e-01 4755.4292 0.9983098
## theta[689] 2.795305e-01 0.0002816740 0.01944191 2.418676e-01 2.668373e-01 2.791996e-01 2.918459e-01 3.188176e-01 4764.1369 0.9983951
## theta[690] 1.207074e-01 0.0005384024 0.03407683 6.129761e-02 9.709012e-02 1.175942e-01 1.416865e-01 1.942096e-01 4005.9394 0.9983140
## theta[691] 2.804359e-01 0.0002717008 0.01802590 2.476583e-01 2.679444e-01 2.797417e-01 2.933410e-01 3.144958e-01 4401.6135 0.9984443
## theta[692] 2.063441e-01 0.0004865292 0.02620088 1.570845e-01 1.879191e-01 2.066117e-01 2.240699e-01 2.572495e-01 2900.1069 0.9989569
## theta[693] 2.909521e-01 0.0002822353 0.01838521 2.570570e-01 2.781417e-01 2.910347e-01 3.034482e-01 3.283146e-01 4243.4064 0.9983416
## theta[694] 9.559228e-02 0.0005423655 0.02688674 4.967136e-02 7.646429e-02 9.312002e-02 1.131905e-01 1.547057e-01 2457.4931 0.9985004
## theta[695] 2.471196e-01 0.0002674011 0.01676270 2.157413e-01 2.357273e-01 2.466714e-01 2.583138e-01 2.815685e-01 3929.7181 0.9987241
## theta[696] 2.816756e-01 0.0003713883 0.02293339 2.369078e-01 2.667557e-01 2.823654e-01 2.969058e-01 3.283420e-01 3813.1177 0.9993242
## theta[697] 2.292841e-01 0.0004925377 0.02921550 1.746680e-01 2.089233e-01 2.285986e-01 2.478199e-01 2.892991e-01 3518.4195 0.9983633
## theta[698] 2.866738e-01 0.0006502843 0.03721170 2.198222e-01 2.596772e-01 2.854511e-01 3.120931e-01 3.625596e-01 3274.5568 0.9985835
## theta[699] 2.714011e-01 0.0005725115 0.03635307 2.069027e-01 2.462878e-01 2.700467e-01 2.955320e-01 3.468549e-01 4031.9371 0.9999442
## theta[700] 2.324090e-01 0.0004230887 0.02490393 1.838343e-01 2.155130e-01 2.321954e-01 2.480362e-01 2.839788e-01 3464.7583 0.9985147
## theta[701] 1.251154e-01 0.0007580496 0.04477834 4.987692e-02 9.305188e-02 1.204203e-01 1.542330e-01 2.253670e-01 3489.3201 0.9983207
## theta[702] 1.352468e-01 0.0008580101 0.04726063 5.824966e-02 1.012338e-01 1.302833e-01 1.623119e-01 2.402725e-01 3033.9902 0.9988130
## theta[703] 2.570981e-01 0.0003156898 0.02129073 2.149330e-01 2.429235e-01 2.566520e-01 2.714060e-01 2.995594e-01 4548.4156 0.9987922
## theta[704] 3.059237e-01 0.0003114755 0.01762289 2.714090e-01 2.935285e-01 3.056560e-01 3.178363e-01 3.410468e-01 3201.1519 0.9988934
## theta[705] 2.550703e-01 0.0003728686 0.02125011 2.142158e-01 2.407608e-01 2.548674e-01 2.686664e-01 3.003590e-01 3247.9599 0.9986496
## theta[706] 2.618028e-01 0.0002868157 0.01811400 2.268964e-01 2.486405e-01 2.616014e-01 2.748928e-01 2.977853e-01 3988.6217 0.9984128
## theta[707] 2.636072e-01 0.0007874467 0.05025823 1.704236e-01 2.281600e-01 2.625866e-01 2.974769e-01 3.673721e-01 4073.5400 0.9983162
## theta[708] 2.553023e-01 0.0002461795 0.01699198 2.222068e-01 2.442651e-01 2.553110e-01 2.661226e-01 2.899986e-01 4764.1369 0.9985826
## theta[709] 2.497809e-01 0.0007016423 0.04535642 1.706368e-01 2.160399e-01 2.485186e-01 2.789151e-01 3.440171e-01 4178.7462 0.9984712
## theta[710] 2.187410e-01 0.0003701322 0.02261696 1.749741e-01 2.035364e-01 2.185803e-01 2.327071e-01 2.649071e-01 3733.8316 0.9989155
## theta[711] 1.650757e-01 0.0008466459 0.04281385 9.259887e-02 1.344479e-01 1.620042e-01 1.908494e-01 2.598631e-01 2557.2017 0.9982990
## theta[712] 1.369646e-01 0.0007498015 0.04701989 5.943675e-02 1.030228e-01 1.331126e-01 1.668915e-01 2.390162e-01 3932.5178 0.9983205
## theta[713] 1.383437e-01 0.0005823845 0.03524085 7.578074e-02 1.135156e-01 1.358599e-01 1.606025e-01 2.151621e-01 3661.6186 0.9987884
## theta[714] 2.418696e-01 0.0003025259 0.02088116 2.034094e-01 2.270847e-01 2.414268e-01 2.563330e-01 2.845793e-01 4764.1369 0.9982754
## theta[715] 2.472117e-01 0.0005476189 0.03779815 1.760872e-01 2.233283e-01 2.450783e-01 2.726434e-01 3.239085e-01 4764.1369 0.9985211
## theta[716] 2.777790e-01 0.0003824898 0.02255153 2.338163e-01 2.623158e-01 2.778194e-01 2.928286e-01 3.222517e-01 3476.2606 0.9995236
## theta[717] 2.176085e-01 0.0007353534 0.04084792 1.373898e-01 1.905199e-01 2.179496e-01 2.429592e-01 3.002044e-01 3085.6580 0.9993733
## theta[718] 1.243688e-01 0.0009993326 0.04611346 4.848287e-02 9.207292e-02 1.197699e-01 1.501355e-01 2.319395e-01 2129.2923 0.9986765
## theta[719] 1.246852e-01 0.0008872051 0.04422122 5.273269e-02 9.253983e-02 1.212637e-01 1.509680e-01 2.263401e-01 2484.3535 0.9994556
## theta[720] 2.389047e-01 0.0004122144 0.02681378 1.880252e-01 2.201440e-01 2.386773e-01 2.573439e-01 2.940293e-01 4231.2596 0.9988613
## theta[721] 1.239795e-01 0.0008860288 0.04586820 4.826655e-02 9.058644e-02 1.197948e-01 1.518202e-01 2.255519e-01 2679.9558 0.9983235
## theta[722] 2.334875e-01 0.0002915002 0.01583916 2.044376e-01 2.220043e-01 2.332084e-01 2.452818e-01 2.646820e-01 2952.4787 0.9983230
## theta[723] 1.452340e-01 0.0006188193 0.03530654 8.198865e-02 1.187113e-01 1.430708e-01 1.699642e-01 2.184466e-01 3255.2375 0.9991100
## theta[724] 1.343105e-01 0.0006855234 0.04225503 6.457078e-02 1.054632e-01 1.303553e-01 1.589625e-01 2.268888e-01 3799.3753 0.9987304
## theta[725] 2.639859e-01 0.0005364754 0.03385044 1.990468e-01 2.412657e-01 2.616810e-01 2.856775e-01 3.364339e-01 3981.3382 0.9991231
## theta[726] 2.426724e-01 0.0005769866 0.03733340 1.757633e-01 2.163837e-01 2.404397e-01 2.670815e-01 3.192838e-01 4186.6207 0.9983674
## theta[727] 1.269880e-01 0.0008232203 0.04495714 5.431076e-02 9.446925e-02 1.224535e-01 1.543816e-01 2.267677e-01 2982.3958 0.9987940
## theta[728] 1.249009e-01 0.0008129457 0.04243114 5.580703e-02 9.321863e-02 1.206661e-01 1.498804e-01 2.184790e-01 2724.2461 1.0000120
## theta[729] 2.176479e-01 0.0002838837 0.01839745 1.840928e-01 2.060020e-01 2.170189e-01 2.293766e-01 2.542835e-01 4199.8542 0.9983677
## theta[730] 3.043983e-01 0.0003202716 0.01755357 2.678787e-01 2.930288e-01 3.040203e-01 3.153451e-01 3.411531e-01 3003.9572 1.0002234
## theta[731] 2.138766e-01 0.0003396832 0.02062880 1.742139e-01 1.997200e-01 2.136689e-01 2.281593e-01 2.544227e-01 3688.0753 0.9988884
## theta[732] 2.773891e-01 0.0003721736 0.02505509 2.302224e-01 2.601525e-01 2.770941e-01 2.940763e-01 3.266783e-01 4532.1143 0.9990099
## theta[733] 1.280367e-01 0.0008855944 0.04343495 5.813859e-02 9.552950e-02 1.251619e-01 1.553923e-01 2.202020e-01 2405.5194 0.9990815
## theta[734] 2.544524e-01 0.0003847888 0.02551116 2.073293e-01 2.367758e-01 2.537963e-01 2.713146e-01 3.066470e-01 4395.5747 0.9987601
## theta[735] 2.467993e-01 0.0005507632 0.03320070 1.811430e-01 2.237767e-01 2.456979e-01 2.692703e-01 3.126029e-01 3633.8307 0.9981830
## theta[736] 8.963923e-02 0.0005893272 0.02853074 4.145847e-02 6.905649e-02 8.696855e-02 1.095441e-01 1.528374e-01 2343.7605 0.9986784
## theta[737] 1.147421e-01 0.0006480217 0.03894746 5.082820e-02 8.663225e-02 1.108078e-01 1.399108e-01 2.010471e-01 3612.2611 0.9983275
## theta[738] 1.489407e-01 0.0005589138 0.03393912 8.983603e-02 1.243087e-01 1.471627e-01 1.691729e-01 2.233996e-01 3687.3258 0.9992138
## theta[739] 2.821130e-01 0.0002888247 0.01839936 2.460221e-01 2.699999e-01 2.824707e-01 2.939202e-01 3.187977e-01 4058.2308 0.9984871
## theta[740] 2.591108e-01 0.0004741734 0.03272874 2.000442e-01 2.347471e-01 2.568369e-01 2.833193e-01 3.248146e-01 4764.1369 0.9985563
## theta[741] 2.155070e-01 0.0002632679 0.01817147 1.806239e-01 2.037134e-01 2.152010e-01 2.279072e-01 2.519786e-01 4764.1369 0.9981527
## theta[742] 1.155708e-01 0.0005771325 0.03298456 6.005247e-02 9.153644e-02 1.127614e-01 1.364837e-01 1.860821e-01 3266.4075 0.9997812
## theta[743] 2.688912e-01 0.0003370935 0.01928131 2.330378e-01 2.559288e-01 2.687338e-01 2.814617e-01 3.066695e-01 3271.6926 1.0014698
## theta[744] 2.300685e-01 0.0004238517 0.02603997 1.802492e-01 2.118733e-01 2.290949e-01 2.480611e-01 2.812751e-01 3774.4451 0.9989685
## theta[745] 2.671791e-01 0.0003712305 0.02260070 2.249414e-01 2.515129e-01 2.662817e-01 2.822407e-01 3.140523e-01 3706.4340 0.9990080
## theta[746] 2.299931e-01 0.0003219346 0.02222080 1.884301e-01 2.148451e-01 2.293535e-01 2.445634e-01 2.745055e-01 4764.1369 0.9989202
## theta[747] 2.443711e-01 0.0005029875 0.03129673 1.879697e-01 2.229813e-01 2.439484e-01 2.645290e-01 3.081107e-01 3871.5371 0.9987663
## theta[748] 2.476239e-01 0.0007033169 0.04424565 1.630605e-01 2.168892e-01 2.472766e-01 2.754355e-01 3.402914e-01 3957.6653 0.9981619
## theta[749] 1.879731e-01 0.0004793460 0.02516375 1.401549e-01 1.710413e-01 1.869438e-01 2.054233e-01 2.396507e-01 2755.8309 0.9991719
## theta[750] 2.700157e-01 0.0002897557 0.01988879 2.317577e-01 2.557648e-01 2.700887e-01 2.829877e-01 3.094501e-01 4711.4335 0.9984456
## theta[751] 1.262984e-01 0.0008893005 0.04656471 5.050331e-02 9.182387e-02 1.227092e-01 1.541465e-01 2.298334e-01 2741.6802 0.9990759
## theta[752] 1.955322e-01 0.0003953798 0.02324612 1.507515e-01 1.793123e-01 1.955959e-01 2.110949e-01 2.415092e-01 3456.7820 0.9985571
## theta[753] 2.377033e-01 0.0002733727 0.01842153 2.021006e-01 2.252260e-01 2.369635e-01 2.494456e-01 2.740365e-01 4540.8910 0.9983596
## theta[754] 2.595939e-01 0.0004212766 0.02438462 2.122007e-01 2.428952e-01 2.590557e-01 2.752932e-01 3.105131e-01 3350.4043 0.9985390
## theta[755] 2.645299e-01 0.0003089118 0.02086479 2.247948e-01 2.501496e-01 2.641016e-01 2.780250e-01 3.040324e-01 4562.0426 0.9984794
## theta[756] 1.105994e-01 0.0005085100 0.02954248 5.939966e-02 9.065966e-02 1.086209e-01 1.281209e-01 1.742839e-01 3375.1645 0.9988441
## theta[757] 1.279472e-01 0.0007524250 0.04308125 5.736438e-02 9.660786e-02 1.239165e-01 1.544054e-01 2.214482e-01 3278.3104 0.9985374
## theta[758] 2.472465e-01 0.0004946978 0.03060342 1.887449e-01 2.263928e-01 2.460937e-01 2.675493e-01 3.081770e-01 3827.0146 0.9987277
## theta[759] 2.780942e-01 0.0002833126 0.01787366 2.428582e-01 2.657853e-01 2.777006e-01 2.901813e-01 3.146959e-01 3980.1124 0.9981932
## theta[760] 2.866638e-01 0.0003436456 0.02371935 2.400951e-01 2.710491e-01 2.860999e-01 3.020954e-01 3.330140e-01 4764.1369 0.9989611
## theta[761] 2.561808e-01 0.0005287280 0.03071199 2.003022e-01 2.345530e-01 2.546623e-01 2.775707e-01 3.180783e-01 3374.0488 0.9986924
## theta[762] 1.277245e-01 0.0008059966 0.04519387 5.181695e-02 9.597945e-02 1.231141e-01 1.563372e-01 2.328383e-01 3144.0730 0.9991685
## theta[763] 2.474215e-01 0.0006696690 0.03833632 1.742424e-01 2.206789e-01 2.460646e-01 2.720697e-01 3.273883e-01 3277.1817 0.9984970
## theta[764] 1.404186e-01 0.0009369688 0.04822311 5.892042e-02 1.081199e-01 1.357352e-01 1.690347e-01 2.516023e-01 2648.8667 1.0003603
## theta[765] 2.111514e-01 0.0004726464 0.03117518 1.506668e-01 1.904631e-01 2.101591e-01 2.318974e-01 2.742367e-01 4350.5596 0.9999095
## theta[766] 1.289248e-01 0.0007403429 0.04282102 5.911523e-02 9.738085e-02 1.239965e-01 1.558172e-01 2.214509e-01 3345.4004 0.9990354
## theta[767] 1.350003e-01 0.0007848783 0.04705276 5.812946e-02 1.001190e-01 1.310540e-01 1.645451e-01 2.411774e-01 3593.8970 0.9988098
## theta[768] 2.588546e-01 0.0003131034 0.01952165 2.225721e-01 2.453441e-01 2.584994e-01 2.722249e-01 2.977940e-01 3887.3863 0.9989348
## theta[769] 1.252404e-01 0.0006949019 0.04355582 5.228709e-02 9.343104e-02 1.213678e-01 1.529455e-01 2.213695e-01 3928.6694 0.9983345
## theta[770] 2.569218e-01 0.0003758892 0.02594490 2.082903e-01 2.388890e-01 2.569113e-01 2.737866e-01 3.103064e-01 4764.1369 0.9989639
## theta[771] 2.813618e-01 0.0003815852 0.02633805 2.313648e-01 2.622234e-01 2.814791e-01 3.000645e-01 3.318932e-01 4764.1369 0.9983459
## theta[772] 2.481369e-01 0.0003972802 0.02210536 2.043029e-01 2.328834e-01 2.473671e-01 2.639595e-01 2.921078e-01 3096.0009 0.9988424
## theta[773] 2.258641e-01 0.0005853657 0.03283951 1.612528e-01 2.040068e-01 2.241611e-01 2.477546e-01 2.900172e-01 3147.3037 0.9987032
## theta[774] 2.316332e-01 0.0006632814 0.04251432 1.544407e-01 2.031104e-01 2.307594e-01 2.579738e-01 3.193129e-01 4108.4209 0.9999267
## theta[775] 2.226116e-01 0.0003387795 0.01964716 1.852447e-01 2.092514e-01 2.222256e-01 2.356372e-01 2.610584e-01 3363.2999 0.9985809
## theta[776] 2.416199e-01 0.0003148578 0.01820810 2.072778e-01 2.283588e-01 2.412515e-01 2.541097e-01 2.775876e-01 3344.2605 0.9987732
## theta[777] 1.273721e-01 0.0008637040 0.04486076 5.271175e-02 9.549869e-02 1.234112e-01 1.550886e-01 2.283134e-01 2697.7597 0.9987276
## theta[778] 2.538193e-01 0.0004371491 0.02858168 2.003711e-01 2.352680e-01 2.536196e-01 2.721999e-01 3.101219e-01 4274.8048 0.9987143
## theta[779] 2.556041e-01 0.0002519531 0.01633744 2.244579e-01 2.448254e-01 2.554884e-01 2.669585e-01 2.872850e-01 4204.6384 0.9982695
## theta[780] 1.185508e-01 0.0005606106 0.03328151 6.070063e-02 9.552791e-02 1.166012e-01 1.395296e-01 1.909738e-01 3524.3858 0.9991619
## theta[781] 1.585763e-01 0.0009114671 0.04928751 7.720481e-02 1.222796e-01 1.535863e-01 1.891995e-01 2.635655e-01 2924.0970 0.9987357
## theta[782] 2.163291e-01 0.0003623871 0.02258872 1.759860e-01 2.001848e-01 2.160114e-01 2.321754e-01 2.576933e-01 3885.4195 0.9989563
## theta[783] 2.677220e-01 0.0003691319 0.02270207 2.241947e-01 2.520677e-01 2.667464e-01 2.840967e-01 3.128794e-01 3782.4022 0.9989723
## theta[784] 2.792347e-01 0.0002658896 0.01699675 2.470117e-01 2.679564e-01 2.789367e-01 2.908778e-01 3.135185e-01 4086.2873 0.9986715
## theta[785] 2.528470e-01 0.0004308227 0.02580428 2.042815e-01 2.346829e-01 2.525953e-01 2.695794e-01 3.060957e-01 3587.4528 1.0011807
## theta[786] 2.298423e-01 0.0003347970 0.02102825 1.872870e-01 2.159436e-01 2.290119e-01 2.436264e-01 2.714587e-01 3944.9629 0.9987582
## theta[787] 1.477805e-01 0.0008878318 0.04518763 7.059981e-02 1.150703e-01 1.449934e-01 1.761795e-01 2.456066e-01 2590.4652 1.0000478
## theta[788] 1.986874e-01 0.0008183594 0.04090195 1.252167e-01 1.692656e-01 1.967135e-01 2.235286e-01 2.835612e-01 2498.0426 0.9984088
## theta[789] 1.873276e-01 0.0007081344 0.03849653 1.143715e-01 1.615932e-01 1.858138e-01 2.132951e-01 2.673755e-01 2955.3686 0.9987469
## theta[790] 1.253355e-01 0.0007031964 0.04548849 4.654266e-02 9.451503e-02 1.189413e-01 1.523793e-01 2.286771e-01 4184.5608 0.9996417
## theta[791] 2.121474e-01 0.0003655287 0.02462759 1.674342e-01 1.952167e-01 2.108104e-01 2.291898e-01 2.619820e-01 4539.4246 0.9981952
## theta[792] 1.253807e-01 0.0007566878 0.04686375 4.781873e-02 9.170434e-02 1.201209e-01 1.539215e-01 2.299312e-01 3835.6649 0.9983554
## theta[793] 2.422859e-01 0.0004030784 0.02723733 1.919202e-01 2.231109e-01 2.420102e-01 2.621726e-01 2.983327e-01 4566.1490 0.9987613
## theta[794] 2.462101e-01 0.0007046940 0.04034337 1.744892e-01 2.183044e-01 2.446081e-01 2.729972e-01 3.286909e-01 3277.5039 0.9988863
## theta[795] 2.354308e-01 0.0006987624 0.04283038 1.582167e-01 2.039997e-01 2.344020e-01 2.650816e-01 3.202813e-01 3757.0305 0.9985386
## theta[796] 2.216834e-01 0.0005108727 0.03277010 1.613913e-01 1.987024e-01 2.200491e-01 2.434333e-01 2.870886e-01 4114.6246 0.9989686
## theta[797] 2.176153e-01 0.0004933657 0.02846210 1.647169e-01 1.983225e-01 2.171916e-01 2.374061e-01 2.763445e-01 3328.0975 0.9994705
## theta[798] 2.063013e-01 0.0005390706 0.03361823 1.437550e-01 1.828943e-01 2.063494e-01 2.275538e-01 2.761938e-01 3889.1834 0.9996229
## theta[799] 1.142621e-01 0.0007331631 0.03728719 5.168018e-02 8.765834e-02 1.099010e-01 1.372585e-01 1.959160e-01 2586.5332 0.9992827
## theta[800] 2.424573e-01 0.0007075483 0.04443255 1.607656e-01 2.122294e-01 2.418412e-01 2.710982e-01 3.379102e-01 3943.5767 0.9997660
## theta[801] 2.438504e-01 0.0006132941 0.03749015 1.764635e-01 2.176125e-01 2.427088e-01 2.685285e-01 3.226634e-01 3736.7732 0.9989178
## theta[802] 1.249892e-01 0.0008487426 0.04400982 4.797798e-02 9.453339e-02 1.212038e-01 1.505586e-01 2.217888e-01 2688.7301 0.9984356
## theta[803] 2.440465e-01 0.0008715834 0.04393445 1.635363e-01 2.133518e-01 2.417535e-01 2.712055e-01 3.363515e-01 2540.9289 0.9998467
## theta[804] 1.724091e-01 0.0007473889 0.03691914 1.078572e-01 1.449045e-01 1.697864e-01 1.970576e-01 2.523914e-01 2440.1130 0.9990949
## theta[805] 1.085876e-01 0.0005644210 0.02889732 5.850377e-02 8.808156e-02 1.064892e-01 1.269199e-01 1.704958e-01 2621.2512 0.9981958
## theta[806] 1.272149e-01 0.0008534948 0.04491523 5.170261e-02 9.429337e-02 1.228541e-01 1.555116e-01 2.289059e-01 2769.3988 1.0001926
## theta[807] 2.690939e-01 0.0002859887 0.01955446 2.309741e-01 2.560543e-01 2.688983e-01 2.815878e-01 3.089655e-01 4675.1350 0.9988327
## theta[808] 2.414454e-01 0.0003684990 0.02355700 1.959721e-01 2.253696e-01 2.411935e-01 2.565547e-01 2.914032e-01 4086.6485 0.9985855
## theta[809] 1.282497e-01 0.0007637238 0.04474088 5.234533e-02 9.729922e-02 1.232119e-01 1.559406e-01 2.263558e-01 3431.9141 0.9994819
## theta[810] 1.509775e-01 0.0009257799 0.04798496 7.309860e-02 1.163635e-01 1.461615e-01 1.802096e-01 2.564817e-01 2686.5494 0.9987541
## theta[811] 1.278448e-01 0.0008291118 0.04550291 5.292559e-02 9.604679e-02 1.224548e-01 1.569816e-01 2.249392e-01 3011.9804 1.0006135
## theta[812] 7.595610e-02 0.0006965240 0.02643823 3.092930e-02 5.705766e-02 7.390902e-02 9.208346e-02 1.348104e-01 1440.7630 0.9993553
## theta[813] 1.287150e-01 0.0007930023 0.04588769 5.081707e-02 9.544001e-02 1.237928e-01 1.578238e-01 2.291486e-01 3348.4482 0.9982894
## theta[814] 1.368450e-01 0.0007627739 0.04642750 6.092708e-02 1.037439e-01 1.305582e-01 1.669656e-01 2.443388e-01 3704.7500 0.9987156
## theta[815] 2.536348e-01 0.0005298384 0.03306102 1.913001e-01 2.314920e-01 2.530511e-01 2.759059e-01 3.196958e-01 3893.5497 0.9995555
## theta[816] 2.611566e-01 0.0004351950 0.02753509 2.107236e-01 2.427573e-01 2.611899e-01 2.794912e-01 3.158031e-01 4003.1793 0.9994727
## theta[817] 1.245191e-01 0.0008550364 0.04544057 4.781661e-02 9.143617e-02 1.205573e-01 1.505929e-01 2.292490e-01 2824.3483 0.9991108
## theta[818] 2.488853e-01 0.0005201118 0.03161961 1.900679e-01 2.257535e-01 2.487216e-01 2.707427e-01 3.110175e-01 3695.8956 0.9981262
## theta[819] 1.272871e-01 0.0007634055 0.04625981 4.980649e-02 9.358616e-02 1.227808e-01 1.557884e-01 2.334124e-01 3671.9541 0.9993454
## theta[820] 3.038400e-01 0.0002645752 0.01754944 2.700496e-01 2.915281e-01 3.037715e-01 3.160014e-01 3.406201e-01 4399.7520 0.9984238
## theta[821] 1.198541e-01 0.0007821919 0.04118766 5.423409e-02 8.884115e-02 1.157243e-01 1.456608e-01 2.125511e-01 2772.7303 0.9995153
## theta[822] 2.368753e-01 0.0005673791 0.03226279 1.756222e-01 2.146802e-01 2.364895e-01 2.582176e-01 3.025441e-01 3233.3846 0.9983125
## theta[823] 2.545019e-01 0.0004385256 0.02807574 2.036635e-01 2.351364e-01 2.539376e-01 2.727870e-01 3.109243e-01 4098.9489 0.9988433
## theta[824] 2.558793e-01 0.0004257273 0.02626750 2.061297e-01 2.379406e-01 2.548641e-01 2.721791e-01 3.125125e-01 3806.9266 0.9985166
## theta[825] 1.565361e-01 0.0006288952 0.03538340 9.186159e-02 1.321917e-01 1.548862e-01 1.782233e-01 2.299735e-01 3165.5012 0.9985473
## theta[826] 2.321174e-01 0.0004988854 0.02833442 1.792840e-01 2.128009e-01 2.311388e-01 2.509125e-01 2.883709e-01 3225.7230 0.9988959
## theta[827] 1.192491e-01 0.0008110947 0.04188005 5.160345e-02 8.950543e-02 1.148352e-01 1.461488e-01 2.114865e-01 2666.0678 0.9992519
## theta[828] 1.247247e-01 0.0005133825 0.02983440 7.293594e-02 1.043144e-01 1.231528e-01 1.429914e-01 1.898164e-01 3377.1672 0.9985221
## theta[829] 2.382941e-01 0.0003182561 0.01910086 2.022259e-01 2.252411e-01 2.382037e-01 2.516653e-01 2.766322e-01 3602.0729 0.9997932
## theta[830] 2.737817e-01 0.0004063601 0.02804808 2.220654e-01 2.541280e-01 2.734574e-01 2.916635e-01 3.304384e-01 4764.1369 0.9985743
## theta[831] 2.170155e-01 0.0006861147 0.03939730 1.436713e-01 1.898918e-01 2.146897e-01 2.432518e-01 2.958640e-01 3297.1560 0.9996364
## theta[832] 2.392729e-01 0.0003163897 0.02112200 2.007183e-01 2.241082e-01 2.385369e-01 2.530894e-01 2.819455e-01 4456.8219 0.9989088
## theta[833] 1.554134e-01 0.0009133891 0.04409522 7.901242e-02 1.214673e-01 1.532982e-01 1.842988e-01 2.553250e-01 2330.6190 0.9981465
## theta[834] 1.207007e-01 0.0007749543 0.04036503 5.353326e-02 9.104526e-02 1.169257e-01 1.452638e-01 2.103788e-01 2713.0538 1.0003686
## theta[835] 2.834899e-01 0.0003389490 0.01973652 2.472575e-01 2.689573e-01 2.833333e-01 2.978595e-01 3.212925e-01 3390.5694 0.9982781
## theta[836] 2.253431e-01 0.0004297514 0.02899317 1.729652e-01 2.053731e-01 2.242979e-01 2.446462e-01 2.846742e-01 4551.5228 0.9981425
## theta[837] 2.507090e-01 0.0008776980 0.04693569 1.619064e-01 2.183246e-01 2.490635e-01 2.818542e-01 3.511994e-01 2859.6723 0.9980557
## theta[838] 2.340045e-01 0.0003258113 0.02179095 1.918520e-01 2.190385e-01 2.338806e-01 2.480934e-01 2.783725e-01 4473.2185 0.9990331
## theta[839] 2.574808e-01 0.0004067875 0.02807758 2.048664e-01 2.370858e-01 2.566789e-01 2.766123e-01 3.138926e-01 4764.1369 0.9983603
## theta[840] 2.432352e-01 0.0004618136 0.02625304 1.961480e-01 2.240894e-01 2.427995e-01 2.612710e-01 2.965292e-01 3231.6622 0.9988525
## theta[841] 1.123728e-01 0.0008358231 0.03995325 4.205875e-02 8.441885e-02 1.100512e-01 1.362229e-01 2.022027e-01 2284.9433 0.9984816
## theta[842] 1.336592e-01 0.0007685492 0.04308309 5.975699e-02 1.039623e-01 1.292770e-01 1.582431e-01 2.323093e-01 3142.4640 0.9992038
## theta[843] 1.259984e-01 0.0007671916 0.04683335 4.929421e-02 9.166909e-02 1.208954e-01 1.543120e-01 2.304621e-01 3726.5141 0.9998227
## theta[844] 1.141554e-01 0.0006872559 0.04076330 4.689220e-02 8.393327e-02 1.094939e-01 1.402193e-01 2.004859e-01 3518.0474 0.9993393
## theta[845] 1.127907e-01 0.0006348196 0.03202556 5.646811e-02 8.939087e-02 1.103362e-01 1.328917e-01 1.788895e-01 2545.0286 0.9997228
## theta[846] 2.369390e-01 0.0003463685 0.02246011 1.947594e-01 2.218776e-01 2.363301e-01 2.516106e-01 2.821616e-01 4204.8171 0.9993722
## theta[847] 1.298882e-01 0.0008673164 0.04518500 5.501186e-02 9.657317e-02 1.263013e-01 1.574622e-01 2.346750e-01 2714.1471 0.9997339
## theta[848] 1.561337e-01 0.0008622652 0.04715666 7.551755e-02 1.246145e-01 1.523044e-01 1.834296e-01 2.649006e-01 2990.9172 0.9997565
## theta[849] 2.117162e-01 0.0005016311 0.03151404 1.521069e-01 1.916580e-01 2.106970e-01 2.329214e-01 2.746179e-01 3946.7456 0.9981267
## theta[850] 1.433616e-01 0.0008536864 0.05053947 6.103042e-02 1.065760e-01 1.378075e-01 1.760305e-01 2.570508e-01 3504.8114 0.9984327
## theta[851] 1.212212e-01 0.0007487005 0.04172197 5.272107e-02 9.106179e-02 1.164706e-01 1.468460e-01 2.120830e-01 3105.3697 0.9984855
## theta[852] 1.508743e-01 0.0005503862 0.03076205 9.793167e-02 1.293644e-01 1.482009e-01 1.695101e-01 2.179278e-01 3123.8890 0.9996961
## theta[853] 9.503248e-02 0.0006042959 0.02761127 4.718501e-02 7.579488e-02 9.333898e-02 1.116659e-01 1.551230e-01 2087.7249 0.9985589
## theta[854] 2.563473e-01 0.0004648313 0.02735563 2.048484e-01 2.376333e-01 2.561318e-01 2.731027e-01 3.133672e-01 3463.3991 0.9984640
## theta[855] 1.225719e-01 0.0008625985 0.04278978 5.114008e-02 9.162967e-02 1.182280e-01 1.487188e-01 2.196480e-01 2460.7237 0.9997870
## theta[856] 2.665715e-01 0.0005558926 0.03164785 2.045407e-01 2.447225e-01 2.672271e-01 2.869778e-01 3.295029e-01 3241.2055 0.9985787
## theta[857] 2.647598e-01 0.0003281712 0.02001381 2.266352e-01 2.516249e-01 2.642843e-01 2.774905e-01 3.066644e-01 3719.2775 0.9989308
## theta[858] 2.795222e-01 0.0003396950 0.02344668 2.336699e-01 2.627016e-01 2.796466e-01 2.956082e-01 3.232228e-01 4764.1369 0.9984418
## theta[859] 2.363996e-01 0.0004480298 0.02775303 1.866044e-01 2.162756e-01 2.354196e-01 2.555088e-01 2.928024e-01 3837.1348 0.9987432
## theta[860] 2.624808e-01 0.0002855318 0.01970819 2.244876e-01 2.495525e-01 2.625540e-01 2.754863e-01 3.017533e-01 4764.1369 0.9993509
## theta[861] 2.903802e-01 0.0003318338 0.02290408 2.452872e-01 2.756466e-01 2.898278e-01 3.046219e-01 3.364326e-01 4764.1369 0.9984519
## theta[862] 2.070613e-01 0.0006614545 0.03441192 1.394605e-01 1.846600e-01 2.060853e-01 2.297485e-01 2.779534e-01 2706.5613 0.9990203
## theta[863] 2.599903e-01 0.0003244742 0.02202924 2.187093e-01 2.441014e-01 2.595118e-01 2.747371e-01 3.021020e-01 4609.3388 0.9983748
## theta[864] 2.549510e-01 0.0005356163 0.03353933 1.952164e-01 2.303375e-01 2.534071e-01 2.785407e-01 3.213691e-01 3921.0387 0.9985850
## theta[865] 2.171739e-01 0.0003819694 0.02376779 1.727025e-01 2.006020e-01 2.171056e-01 2.336291e-01 2.641064e-01 3871.8659 0.9991986
## theta[866] 1.270873e-01 0.0008320595 0.04206358 5.472441e-02 9.829017e-02 1.237805e-01 1.514006e-01 2.235069e-01 2555.6642 1.0006880
## theta[867] 2.350326e-01 0.0004615335 0.03042954 1.784160e-01 2.132818e-01 2.344177e-01 2.551680e-01 2.962237e-01 4346.9485 0.9985900
## theta[868] 1.265135e-01 0.0008339965 0.04459272 5.471731e-02 9.492045e-02 1.213104e-01 1.527839e-01 2.221939e-01 2858.9036 0.9984670
## theta[869] 2.103354e-01 0.0004025541 0.02434053 1.652884e-01 1.939716e-01 2.100620e-01 2.269273e-01 2.574727e-01 3656.0450 0.9988879
## theta[870] 2.773761e-01 0.0004966255 0.03226705 2.155778e-01 2.536704e-01 2.776373e-01 2.994225e-01 3.394815e-01 4221.4387 0.9987853
## theta[871] 3.030140e-01 0.0002867549 0.01851091 2.683949e-01 2.901465e-01 3.028662e-01 3.152082e-01 3.383373e-01 4167.0997 0.9987055
## theta[872] 2.207685e-01 0.0004972700 0.03362913 1.561244e-01 1.978715e-01 2.198045e-01 2.422201e-01 2.902269e-01 4573.4791 0.9986058
## theta[873] 2.285934e-01 0.0004669986 0.02934336 1.715245e-01 2.084518e-01 2.290482e-01 2.479244e-01 2.872966e-01 3948.1046 0.9992967
## theta[874] 2.798020e-01 0.0004250731 0.02770398 2.250165e-01 2.609178e-01 2.793999e-01 2.989422e-01 3.339820e-01 4247.7323 0.9986515
## theta[875] 2.845061e-01 0.0003261216 0.01822910 2.511809e-01 2.715215e-01 2.844348e-01 2.968317e-01 3.204283e-01 3124.4329 0.9998398
## theta[876] 2.702243e-01 0.0002627403 0.01813505 2.338314e-01 2.578764e-01 2.699776e-01 2.823115e-01 3.084675e-01 4764.1369 0.9987387
## theta[877] 2.296438e-01 0.0003774549 0.02447664 1.824499e-01 2.132008e-01 2.289698e-01 2.457737e-01 2.824082e-01 4205.0730 0.9992005
## theta[878] 1.474465e-01 0.0006453020 0.03216515 9.112330e-02 1.246620e-01 1.456218e-01 1.690893e-01 2.158319e-01 2484.5354 0.9995130
## theta[879] 1.398035e-01 0.0007333818 0.04507674 6.174660e-02 1.073476e-01 1.345579e-01 1.699473e-01 2.379027e-01 3777.8504 0.9982704
## theta[880] 2.522902e-01 0.0002694868 0.01692928 2.197653e-01 2.405954e-01 2.522279e-01 2.638883e-01 2.847388e-01 3946.4074 0.9995610
## theta[881] 2.360164e-01 0.0003427202 0.02363720 1.914291e-01 2.191998e-01 2.359594e-01 2.519600e-01 2.818120e-01 4756.7763 0.9987359
## theta[882] 1.330643e-01 0.0008126997 0.04723548 5.534014e-02 1.018556e-01 1.279565e-01 1.598037e-01 2.424258e-01 3378.1306 0.9989830
## theta[883] 1.240558e-01 0.0008428601 0.04440050 4.983377e-02 9.286668e-02 1.192982e-01 1.485227e-01 2.288409e-01 2775.0112 0.9984793
## theta[884] 2.391093e-01 0.0006152919 0.04246912 1.622766e-01 2.098418e-01 2.378214e-01 2.670647e-01 3.257824e-01 4764.1369 0.9983855
## theta[885] 2.464988e-01 0.0002435004 0.01680706 2.141437e-01 2.350507e-01 2.459129e-01 2.575327e-01 2.801317e-01 4764.1369 0.9987138
## theta[886] 1.591984e-01 0.0007028454 0.04140510 8.763941e-02 1.312280e-01 1.556917e-01 1.839483e-01 2.490648e-01 3470.4684 0.9985083
## gamma[1] -1.091651e+00 0.0007905820 0.03537473 -1.161536e+00 -1.115025e+00 -1.090552e+00 -1.067571e+00 -1.021673e+00 2002.1301 1.0017626
## gamma[2] -1.097177e+00 0.0008289421 0.03907645 -1.176770e+00 -1.122468e+00 -1.096951e+00 -1.071784e+00 -1.024104e+00 2222.1932 0.9998557
## gamma[3] -1.069081e+00 0.0006909335 0.03324049 -1.132630e+00 -1.092748e+00 -1.068696e+00 -1.047504e+00 -1.004791e+00 2314.5277 0.9997269
## gamma[4] -1.170030e+00 0.0007994678 0.03539344 -1.240765e+00 -1.192883e+00 -1.169619e+00 -1.146399e+00 -1.104135e+00 1959.9436 1.0001908
## gamma[5] -1.050173e+00 0.0009541371 0.03916198 -1.129979e+00 -1.077133e+00 -1.050237e+00 -1.024434e+00 -9.743179e-01 1684.6423 1.0000972
## gamma[6] -1.107683e+00 0.0007201833 0.03140448 -1.172541e+00 -1.129068e+00 -1.107056e+00 -1.085559e+00 -1.048665e+00 1901.5040 0.9992246
## gamma[7] -1.910327e+00 0.0024500712 0.05708249 -2.020372e+00 -1.947511e+00 -1.911070e+00 -1.870077e+00 -1.802286e+00 542.8108 1.0035191
## gamma[8] -1.054927e+00 0.0009197498 0.03865135 -1.133037e+00 -1.080092e+00 -1.054404e+00 -1.029045e+00 -9.800656e-01 1765.9970 0.9986652
## gamma[9] -1.104083e+00 0.0009982007 0.04181421 -1.189718e+00 -1.131950e+00 -1.102983e+00 -1.076656e+00 -1.025579e+00 1754.7373 0.9989844
## alpha_w 2.049676e-02 0.0004108001 0.01745399 -1.340492e-02 9.257595e-03 2.071060e-02 3.258175e-02 5.315404e-02 1805.2128 1.0006108
## alpha_h -9.700853e-03 0.0004146935 0.01679267 -4.196653e-02 -2.112763e-02 -9.784652e-03 1.439943e-03 2.429819e-02 1639.7783 1.0021566
## kappa[1] 1.073369e+02 0.6112569762 23.16902526 6.971627e+01 9.115426e+01 1.047902e+02 1.208600e+02 1.593637e+02 1436.7059 1.0016171
## kappa[2] 1.043715e+02 0.6406791673 24.26721462 6.306153e+01 8.655679e+01 1.019539e+02 1.192425e+02 1.586246e+02 1434.6919 1.0038683
## kappa[3] 9.716261e+01 0.5734302455 20.93812699 6.295223e+01 8.229606e+01 9.498135e+01 1.097060e+02 1.434381e+02 1333.2588 1.0011472
## kappa[4] 9.099094e+01 0.6754700335 19.92277718 5.666480e+01 7.793669e+01 8.885483e+01 1.025654e+02 1.367810e+02 869.9366 1.0050622
## kappa[5] 9.310357e+01 0.6122438986 21.07456643 5.709713e+01 7.746350e+01 9.135139e+01 1.059954e+02 1.378341e+02 1184.8636 0.9994984
## kappa[6] 1.057961e+02 0.7154399239 22.64204151 6.706051e+01 8.898902e+01 1.042585e+02 1.197122e+02 1.558970e+02 1001.5781 0.9995559
## kappa[7] 5.549164e+01 1.2936330975 14.24024358 3.363938e+01 4.530643e+01 5.369662e+01 6.343142e+01 9.093293e+01 121.1749 1.0079337
## kappa[8] 1.098204e+02 0.6514618767 25.19801855 6.719365e+01 9.124733e+01 1.080589e+02 1.255475e+02 1.615100e+02 1496.0798 1.0001329
## kappa[9] 8.919671e+01 0.5928389060 21.64802366 5.143198e+01 7.405744e+01 8.721235e+01 1.029605e+02 1.355706e+02 1333.4082 0.9988656
## lp__ -8.739899e+04 3.6528452961 40.32669990 -8.747462e+04 -8.742666e+04 -8.740072e+04 -8.737193e+04 -8.731784e+04 121.8773 1.0076574Pitchers 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
It doesn’t look like batting average varies substantially with height or weight, if at all.
Changing the model from a Beta prior on class means to a logistic transform of a Normal prior did not substantially affect the results.