Parameter Conditionally Existent on another Parameters

Modeling
1

Hello everyone,

In essence, I am trying to make a massive model comparison job tractable.

I have a model “myModel” that I want to describe some data y. I want the model to behave in a piecewise fashion, changing its behaviour between breakpoints defined in u. However, I do not know in advance how many breakpoints there are (this is part of what I am interested in, as well as their position).

Hence, I have an integer parameter n (the number of breakpoints) that can be any value between 1 and max_n. As n is the number of breakpoints the value of the breakpoints in u are only relevant if they are the first n values.

As n is an integer it has to be marginalized out, hence the sum over the log_likelihoods.

My question is whether this is a valid way of having the values of u conditionally used (based on n) or if this is going to cause havoc with sampling and convergence because the values of u at indexes lower than n are not going to have any impact on the likelihood yet they have been sampled.

data {
  int<lower=1> max_n; // Maximum possible value of n
  int<lower=1> n_data; // Number of data points
  vector[n_data] y; // Observed data
}

parameters {
  vector[max_n] u; // Independent uniform samples for the maximum n
   vector[max_n] full_vector;
}

transformed parameters {
  real log_lik[max_n]; // Log-likelihood for each possible n
  
  for (int n = 1; n <= max_n; n++) {
    
    for (int i = 1:n_max) {
      if (i <= n) {
        full_vector[i] = u[i];
      } else {
        full_vector[i] = 301; // Placeholder for infinity
      }
    }
    
    // Compute likelihood given the data and full_vector
    // Normal likelihood with mean as that is my model that takes vector u
    log_lik[n] = 0; // Reset
    for (int i = 1:n_data; i++) {
      log_lik[n] += normal_lpdf(y[i] | myModel(u), sigma); // Example likelihood
    }
  }
}

model {
  // Uniform prior on the parameters u
  u ~ uniform(0, 1);
  
 sigma ~ uniform(0, 10)

  // Marginalize over all possible n values using the likelihood
  target += log_sum_exp(log_lik);
}