Hi,

I am trying to estimate the difference between two groups. I’ve made the following Stan model,

```
data {
int N1;
real y1[N1];
real y1_mean;
int N2;
real y2[N2];
real y2_mean;
}
parameters {
real<lower=0> mu_tau;
real<lower=0> sigma_tau;
real<lower=0> sigma1;
real<lower=0> sigma2;
real<lower=0> mu_scale1;
real<lower=0> mu_scale2;
real mu1;
real mu2;
}
model {
/* Prior specification */
/* Priors related to mean */
mu_tau ~ normal(0, 1);
mu_scale1 ~ normal(0, mu_tau);
mu_scale2 ~ normal(0, mu_tau);
mu1 ~ normal(y1_mean, mu_scale1);
mu2 ~ normal(y2_mean, mu_scale2);
/* Priors related to scale */
sigma_tau ~ normal(0, 10);
sigma1 ~ normal(0, sigma_tau);
sigma2 ~ normal(0, sigma_tau);
/* Likelihood */
y1 ~ normal(mu1, sigma1);
y2 ~ normal(mu2, sigma2);
}
generated quantities {
real diff_mu;
diff_mu = mu1 - mu2;
}
```

It’s not the prettiest model, but its working. However, as I understand HMC works best with standardized data, i.e. mean=0 and sd=1. In the data I’m working with the mean is between 50-75, and the standard deviation is somewhere in the range 10-15. Thus, it’s a bit hard now to judge what is a informative/non-informative prior.

Are there any tricks I can use here? Standardizing the data and then de-standardizing it after model fit would not make much sense, I believe, since I actually wish to estimate the mean.

Thanks!

David