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 Iâ€™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 Iâ€™m interested in are all > 400.

Do I need to worry about the small bulk and tail ESS for my â€śnuisanceâ€ť parameters, or am I safe to ignore them? My understanding is that the mean/median and quantiles from my â€śnuisanceâ€ť parameters may be unreliable, but since Iâ€™m not interested in estimating them, do I need to worry about the warning?

Kent