I am using a translated and scaled simplex as described in section 1.7 of the Stan Users Guide (v2.24) to center coefficients in a relatively simple multivariate response model. Specifically,
parameters {
...
simplex[N_forms] beta_raw[N_trait];
vector[N_trait] beta_scale;
}
transformed parameters {
vector[N_trait] mu_form[N_forms];
for (i in 1:N_trait) {
for (j in 1:N_forms) {
mu_form[j][i] = beta_scale[i]*(beta_raw[i][j] - 1.0/N_forms);
}
}
...
}
model {
...
for (i in 1:N_trait) {
beta_raw[i] ~ dirichlet(one);
beta_scale[i] ~ normal(0.0, 1.0);
}
...
}
I am combine mu_form
with another linear term to model multivariate mean vectors, but what I’m really interested in is the covariance/correlation matrix associated with those vectors.
My code runs fine, and the diagnostics look good, except that I get a warning about a small bulk and tail ESS. When I examine bulk and tail ESS for each of the parameters in the model, I discover that the warning is because the bulk and tail ESS for beta_raw
and beta_scale
are very small, i.e., 6-20. The bulk and tail ESS for mu_form
are a bit small (< 300), and the bulk and tail ESS for the other linear term is also small (150 or so).
BUT the bulk and tail ESS for all of the parameters I’m interested in are all > 400.
Do I need to worry about the small bulk and tail ESS for my “nuisance” parameters, or am I safe to ignore them? My understanding is that the mean/median and quantiles from my “nuisance” parameters may be unreliable, but since I’m not interested in estimating them, do I need to worry about the warning?
Kent