Happy New Year to everyone.
I have a question about how to write the Non-centered parametrization of lognormal distribution in STAN.
Suppose I have a variable, u ~ lognormal(mu, sigma_u), where mu and sigma_u both > 0 -----> (1)
I also understand that this can also be written as exp(u) ~ normal (mu_normal, sigma_u_normal) —> (2)
So my question is how can write Eq. (1) and (2) as non-centered parameterization in STAN?
For Eq(1), I am not sure, but can I write is -> mu + u_raw*sigma_u? with both mu and u_raw having lognormal distribution priors? I am not sure about it.
And for Eq(2). the non-centered version may be written as exp(mu_normal) + exp(u_raw)*sigma_u_normal ? with normal priors for mu_normal and u_raw?
Any guidance will be highly appreciated.