Heyo!

I am still learning and unsure about centered vs noncentered modelling. I have a simple linear regression model and am trying to understand the modelling with this before I move on to complex stuff.

I had

```
model {
//// priors
beta_0 ~ cauchy(0, 5);
beta ~ cauchy(0, 5);
sigma ~ gamma(0.001, 0.001);
//// likelihood
price ~ normal(beta_0 + x * beta, sigma);
}
```

for now and was wondering if the correct way to non-center this would be:

```
transformed parameters{
vector[n_obs] price_mean;
price_mean = beta_0 + x * beta;
}
model{
//// priors
beta_0 ~ cauchy(0, 5);
beta ~ cauchy(0, 5);
sigma ~ gamma(0.001, 0.001);
//// likelihood
price ~ normal(price_mean, sigma);
}
```

I feel that I am not completely grasping something here. Would this already be â€śreparametrizingâ€ť? I feel that I only gave something a different name - then again, reparametrizing can be just that.

edit: Just for completeness:

price and beta are vectors, beta_0 is a real and x is a matrix. All have the right dimensions, both models run and produce the same results, I would say. As this is not a complex thing, I had expected that and was only looking to get the gist of it.

edit2:

After thinking about it, I would say this is not about non-centering, as I did not split anything up in smaller parts - is that correct?