Problem with initialization

Modeling
1

I am learning to run a Hidden Markov Model with PyStan. I try to specify a model with 3 hidden states with prior transition probabilities as the posterior transition probabilities from a 2 hidden states. The model is like this (it’s incomplete as I leave out parts probably not related to the error encountered):

stan_model =

functions {
 vector normalize(vector x) {
   return x / sum(x);
 }
}

data {
 int<lower=1> T;                   // number of observations (length)
 int<lower=1> K;                   // number of hidden states
 int<lower=1> M;                   // size of the input vector
 int<lower=1> S;                   // number of stocks
 int<lower=1> L;                   // length of flatten array

 real x_t[L];  
 int<lower=1,upper=S> S_idx[L];
 int<lower=1,upper=T> T_idx[L];

 vector[M] u_tm[L];  
}

parameters {
 // Discrete state model
 simplex[K] p_1k;                           // initial state probabilities
 simplex[K] A[K];                           // transistion matrix

 // Continuous observation model
 vector[M] b_km[K];                         // mean regressors
 real<lower=0.001, upper=20> s_k[K];        // residual standard deviations
 real<lower=1,upper=20> nu_k[K];            // residual degrees of freedom
 
 // Prior transition matrix
 vector[2] tran_prob_1;
 vector[2] tran_prob_2;
}

model {
 for(j in 1:K) {
   b_km[j] ~ normal(0, 0.5);
   s_k[j] ~ uniform(0.001, 20);
   nu_k[j] ~ uniform(1,20);
 }
  
 A[1][1:2] ~ dirichlet(tran_prob_1);
 A[2][1:2] ~ dirichlet(tran_prob_2);

 target += log_sum_exp(unalpha_tk[T]); // Note: update based only on last unalpha_tk
}

So the transition probabilities is a 3x3 matrix A. Arrays tran_prob_1 and tran_prob_2 are 2x2 arrays that store dirichlet parameters from the 2 hidden state models.

The StanModel code works OK:
stan_model = pystan.StanModel(model_code=stan_model, verbose=True)

But the model fit encounters a RuntimeError that Initialization failed.
model_fit = stan_model.sampling(data=model_data_dict, iter=800, chains=4, seed=2017)

If I don’t specify the use of posterior transition probabilities, i.e., deleting the part:

  A[1][1:2] ~ dirichlet(tran_prob_1);
  A[2][1:2] ~ dirichlet(tran_prob_2);

then the model runs just fine.
Can you suggest where the problem may be?

2

Dirichlet parameters should be positive so tran_probs need <lower=0> but that alone won’t stop initialization.
The problem is that the simplex constraint on A[1][1:3] does not guarantee that A[1][1:2] is a simplex (and in fact strongly suggests it is not) so it can’t have dirichlet distribution.
What exactly are you trying to do? Is the intended effect that A[1][3]=A[2][3]=0? If so then you’ll have to construct A as a transformed parameter

paramters {
  simplex[2] A1;
  simplex[2] A2;
  simplex[3] A3;
}
transformed parameters {
  simplex[3] A[3];
  A[1] = append_row(A1, 0.0);
  A[2] = append_row(A2, 0.0);
  A[3] = A3;
}