Hello all,

I have a question about the non-centered parameterization of normal distribution. I have two scenarios that I am going to mention and would like your opinion on whether I am on right track or not.

**First Scenario**

data {

vector[N] Y;

}

parameters {

real alpha;

real<lower=0> sigma_y;

vector[N] Y_raw;

}

transformed parameters {

Y = alpha + Y_raw*sigma_y **This is as I understand, the non-centered parameterization**

}

model {

alpha ~ normal(0,2);

sigma_y ~ inv_gamma(1,1);

Y_raw ~ std_normal();

}

**Second Scenario**

data {

vector[N] Y;

}

parameters {

vector[N] alpha;

vector<lower=0>[N] sigma_y;

vector[N] Y_raw;

}

transformed parameters {

Y = alpha + Y_raw .*sigma_y

}

model {

alpha ~ normal(0,2);

sigma_y ~ inv_gamma(1,1);

Y_raw ~ std_normal();

}

**Now I would like to know if my non-centered parameterization in the second scenario is correct or not.**

Thank you all in advance.

Regards

Ants007