Assignment: Your task is to use Rmarkdown to write a short report, readable by a technically literate person. The code you used should not be visible in the final report (unless you have a good reason to show it).
Due: Submit your work via Canvas by the end of the day (midnight) on Thursday, December 3rd. Please submit both the Rmd file and the resulting html or pdf file. You can work with other members of class, but I expect each of you to construct and run all of the scripts yourself.
In class, we looked at the “baseball” dataset: BattingAverage.csv of batting averages of baseball players. To analyze it, we developed and implemented the following Stan model:
data {
int N; // number of players
int hits[N];
int at_bats[N];
int npos; // number of positions
int position[N];
}
parameters {
real<lower=0, upper=1> theta[N];
real<lower=0, upper=1> mu[npos];
real<lower=0> kappa[npos];
}
model {
real alpha;
real beta;
hits ~ binomial(at_bats, theta);
for (i in 1:N) {
alpha = mu[position[i]] * kappa[position[i]];
beta = (1 - mu[position[i]]) * kappa[position[i]];
theta[i] ~ beta(alpha, beta);
}
mu ~ beta(1,1);
kappa ~ gamma(0.1,0.1);
}Please (briefly) describe the data, run the model in Stan, and interpret model and results for an interested baseball fan. In particular, the fan is interested in: the typical batting average and range of variation in batting average by position; how many right fielders have a lower batting average than the 95% quantile of pitchers; and the estimated batting averages of Thomas Field and Prince Fielder (include estimates of uncertainty). (Note that when I say “batting average” I mean potential batting average (\(\theta\)), not realized batting average.)