data {
  int<lower=0> I;
  int<lower=0> n[I];
  int<lower=0> x[I];
  real<lower=0> a;
  real<lower=0> b;
  real m;
  real<lower=0> p;
}

parameters {
  real<lower=0> lambda;
  real mu;
  real<lower=0, upper=1> theta[I];
}

transformed parameters {
  real gam[I];
  for( j in 1:I)
   gam[j] = log(theta[j] / (1-theta[j])) ;
}


model {
  target +=  gamma_lpdf( lambda |  a, b);
  target +=  normal_lpdf( mu | m , 1/sqrt(p));
  target +=  normal_lpdf( gam | mu, 1/sqrt(lambda));
  target +=  binomial_lpmf( x | n , theta);
}

library(rstan)
fit <- stan(
  file = "hospital.stan" ,
  data = dat ,
  iter = 20000,
  warmup = 2000,
  chains = 1
)

structure(
  list(
      I = 12L,
      n = c(47, 211, 810, 148, 196, 360, 119,  207, 97, 256, 148, 215),
      x = c(0, 8, 46, 9, 13, 24, 8, 14, 8, 29, 18, 31),
      a = 2,
      b = 2,
      m = 0,
      p = 0.01),
  .Names = c("I", "n", "x", "a", "b", "m", "p")
)