Hello!

I am fitting a model that contains ordered parameters using an ordered inverse transformation. There is a principled assumption for ordering the parameters and the model fits give me more reasonable parameters when I order them.

But the efficiency and the quality (in terms of parameter recovery using simulated data or actual data) of the fits depends significantly on the priors that I use for the transformed parameter.

I couldn’t find anything about prior distributions on transformed parameters of this kind, so are there typical recommendations? Apologies if this has been addressed and I just failed to find it.

I am fitting the parameters hierarchically, so that session level parameters are constrained by individual level hyperparameters. Here is the relevant part of the code:

```
data{
// number of sessions
int<lower=1> N;
}
parameters {
// hyperparameters (individual level)
vector[2] mu_p;
vector<lower=0>[2] sigma;
// raw session level parameters
vector[N] theta1_raw;
vector[N] theta2_raw;
}
transformed parameters {
// session level parameters
vector<lower=0, upper=1>[N] theta1;
vector<lower=0, upper=1>[N] theta2;
for (n in 1:N) {
// constrain the parameters to (0,1)
theta1[n] = Phi_approx(mu_p[1] + sigma[1] * theta1_raw[n]);
theta2[n] = Phi_approx(mu_p[2] + sigma[2] * (exp(theta2_raw[n]) + theta1_raw[n]));
}
model {
// hyperparameters
mu_p ~ normal(0, 1);
sigma ~ cauchy(0, 5);
// individual parameters
theta1_raw ~ normal(0, 1);
theta2_raw ~ normal(0, 3); //this is the prior in question
...
}
```

Thanks in advance for any advice!