 # Non-Centered parameterizations

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

Hi Ants,

The non-centered parameterisation isn’t used for data, only for parameters. In your example, the non-centered parameterisation isn’t applicable

Hi andrjohns,

I am sorry, I have been lazy about it. I should have indicated it as a random effect parameter.
So if Y is the random effect parameter, would you say that my non-centered parameterization under Second Scenario is still sound, where the mean and standard deviation both are themselves vectors?

Thanks for help,

antony

Yep, the second parameterisation is fine. It assumes that every observation has its own SD, so make sure that is what you’re after. Traditionally a random effect parameter has a single, shared, SD

1 Like

Great one Andrew.
Thanks for your assistance.

Hope all is well in Perth. Looking forward to the trans-Tasman bubble opening up soon :)

Ants