Stan code for inferring probabilities of m-face dice from the number of occurrences of an outcome which is sum of two m-dice's outcomes.

m_dice2.stan

data
{
  int <lower=0> m; // The number of dice faces
  int <lower=0, upper=N> x[2*m-1]; // The numbers of events. x[i] indeicates the number of occurences that a sum of two dices is i+1 in [2,...,2*m].
}

parameters
{
  simplex[m] theta1; // Probability for each face.
  simplex[m] theta2; // Probability for each face.
}

model {
  vector [2*m-1] phi;
  for (s in 2:2*m) {
    phi[s-1] <- 0.;
    for (a in max(1,s-6):min(6,s-1)) {
      phi[s-1] <- phi[s-1]+theta1[a]*theta2[s-a]; // Summing up probabilities that a sum of two dice's outcomes equals s.
    }
  x ~ multinomial(phi);
}