"The parameter has no priors" (but it has?)

General
1

Hello,

My code (see the end of this post for the whole version) produces the following warning:

Messages from stanc:
Warning: The parameter beta_author has no priors.
Warning: The parameter alpha_author has no priors.
Sampling:   0% (4/4400)

However, these messages are gone if I replace this part of the model block:

alpha_author[i,j] ~ normal(mu_alpha[categories[i]], sigma_alpha[categories[i]]);
beta_author[i,j] ~ normal(mu_beta[categories[i]], sigma_beta[categories[i]]);

With these:

alpha_author[i,j] ~ normal(0, 1);
beta_author[i,j] ~ normal(0, 1);

What am I doing wrong?

Full-code below:

data {
    int n_authors;
    int n_years;
    int n_obs;
    int n_topics;
    int n_categories;

    int totals[n_obs];
    int articles[n_obs, n_topics];

    real years[n_obs];
    int authors[n_obs];
    int categories[n_authors];
}

parameters {
    matrix [n_authors, n_topics] alpha_author;
    matrix [n_categories, n_topics] mu_alpha;
    matrix<lower=0> [n_categories, n_topics] sigma_alpha;

    matrix [n_authors, n_topics] beta_author;
    matrix [n_categories, n_topics] mu_beta;
    matrix<lower=0> [n_categories, n_topics] sigma_beta;
}

model {
    for (i in 1:n_categories) {
        for (j in 1:n_topics) {
            mu_alpha[i,j] ~ normal(0, 1);
            sigma_alpha[i,j] ~ exponential(1);
            mu_beta[i,j] ~ normal(0, 1);
            sigma_beta[i,j] ~ exponential(1);
        }
    }

    for (i in 1:n_authors) {
        for (j in 1:n_topics) {
            alpha_author[i,j] ~ normal(mu_alpha[categories[i]], sigma_alpha[categories[i]]);
            beta_author[i,j] ~ normal(mu_beta[categories[i]], sigma_beta[categories[i]]);
            // alpha_author[i,j] ~ normal(0, 1);
            // beta_author[i,j] ~ normal(0, 1);
        }
    }

    for (i in 1:n_obs) {
        for (j in 1:n_topics) {
            real p = Phi(alpha_author[authors[i],j]*years[i] + beta_author[authors[i],j]);
            articles[i,j] ~ binomial(totals[i], p);
        }
    }
}

Thank you for your help (and for this wonderful piece of software!)

2

This is a warning from Stans “pedantic mode” (enabled by default if you are using PyStan) which in this case looks like a false positive, and you can safely ignore it.

3

Thank you very much!