example.Rmd

---
title: "8 Schools Example"
output:
  html_document:
    code_folding: hide
    code_download: true
    toc: true
    toc_float:
      collapsed: false
      smooth_scroll: false

---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

## Stan Code

```{stan output.var="eightschools"}
data {
  int<lower=0> J;         // number of schools 
  real y[J];              // estimated treatment effects
  real<lower=0> sigma[J]; // standard error of effect estimates 
}
parameters {
  real mu;                // population treatment effect
  real<lower=0> tau;      // standard deviation in treatment effects
  vector[J] eta;          // unscaled deviation from mu by school
}
transformed parameters {
  vector[J] theta = mu + tau * eta;        // school treatment effects
}
model {
  target += normal_lpdf(eta | 0, 1);       // prior log-density
  target += normal_lpdf(y | theta, sigma); // log-likelihood
}

```

## Fit

```{r}
library(rstan)
options(mc.cores = parallel::detectCores())
schools_dat <- list(J = 8, 
                    y = c(28,  8, -3,  7, -1,  1, 18, 12),
                    sigma = c(15, 10, 16, 11,  9, 11, 10, 18))

fit <- sampling(object = eightschools, data = schools_dat)
```

## Post processing

```{r}
print(fit)
plot(fit)
pairs(fit, pars = c("mu", "tau", "lp__"))
```