Non-Centered parameterizations

Modeling
1

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

2

Hi Ants,

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

3

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

4

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
5

Great one Andrew.
Thanks for your assistance.

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

Ants