data {
  int<lower=1> I;  // number of question options (22)
  int<lower=0> N;  // number of questions being asked by the user
  int<lower=1> K;  // number of strategies
  // observed "true" questions of the user
  int q[N];
  // array of predicted probabilities of questions given strategies
  // coming from the forward neural network
  matrix[I, K] P_q_S[N];
}
parameters {
  // probabiliy vector of the strategies being applied by the user
  // to be inferred by the model here
  simplex[K] P_S;
}
model {
  for (n in 1:N) {
    // marginal probability vector of the questions being asked
    vector[I] theta = P_q_S[n] * P_S;
    // categorical likelihood
    target += categorical_lpmf(q[n] | theta);
  }
  // priors
  target += dirichlet_lpdf(P_S | rep_vector(1.0, K));
}