bern-with-target.stan

data {
  int<lower=0> N;
  array[N] int<lower=0, upper=1> y;
  real<lower=0> a;
  real<lower=0> b;
}
parameters {
  real<lower=0, upper=1> theta;
}
model {
  // beta prior
  target += (a - 1) * log(theta) + (b - 1) * log(1 - theta);
  
  // likelihood
  for (i in 1:N) {
    target += log(theta) * y[i] + log(1 - theta) * (1 - y[i]);
  }
}