Hidden Markov Model with constraints

Modeling
,
4

Two more ideas!

How about making a custom log_sum_exp that ignores infs:

real log_sum_exp_ignore_inf(vector v) {
  int N = size(v);
  vector noninfs[size(v)];
  int q = 1;

  for (n in 1:N) {
    if (is_inf(v[n]) == 0) {
      noninfs[q] = v[n];
      q =  q + 1;
    }
  }

  return log_sum_exp(noninfs[1:q]);
}

Or make two arrays that encode the possible states at each time sparsely (N time points, 4 states):

int number_of_states_at_T[N] = {
  1,
  2,
  4,
  4,
  ...
}

// -1 is a non-state
int state_ids_at_time_T[N, 4] = {
  {1, -1, -1, -1}, //Only one possible state
  {2, 3, -1, -1}, //Only two possible states
  {1, 2, 3, 4},
  {1, 2, 3, 4},
  ...
}

Then your two inner loops that loop over K now would instead loop over number_of_states_at_T[t] (outer) and number_of_states_at_T[t - 1] (inner). You’d have to account for a variable length log_sum_exp too.