29.3 Poststratification in Stan

The maximum likelihood and Bayesian estimates can be handled with the same Stan program. The model of individual votes is collapsed to a binomial, where \(A_j\) is the number of voters from group \(j\), \(a_j\) is the number of positive responses from group \(j\), and \(N_j\) is the size of group \(j\) in the population.

data {
  int<lower = 1> J;
  int<lower = 0> A[J]; 
  int<lower = 0> a[J];
  vector<lower = 0>[J] N;
parameters {
  vector<lower = 0, upper = 1>[J] theta;
model {
  a ~ binomial(A, theta);
generated quantities {t
  real<lower = 0, upper = 1> phi = dot(N, theta) / sum(N);

The likelihood is vectorized, and implicitly sums over the \(j\). The prior is implicitly uniform on \((0, 1),\) the support of \(\theta.\) The summation is computed using a dot product and the sum function, which is why N was declared as a vector rather than as an array of integers.