Hi community,

I have difficulty in understanding the last section of 10.3 Fitting a Gaussian process | Stan User’s Guide, i.e. Multiple-output Gaussian processes.

In the screenshot, we need to set \alpha=1 to make parameters identifiable.

In the Stan code, \alpha is taken out accordingly by

f = L_K * eta * diag_pre_multiply(alpha, L_Omega)’

```
model {
matrix[N, D] f;
{
matrix[N, N] K = cov_exp_quad(x, 1.0, rho);
matrix[N, N] L_K;
// diagonal elements
for (n in 1:N)
K[n, n] = K[n, n] + delta;
L_K = cholesky_decompose(K);
f = L_K * eta
* diag_pre_multiply(alpha, L_Omega)';
}
```

Sorry that I don’t quite understand why taking \alpha outside of K will make the GP identifiable. And I cannot see the differences made to identifiability. Could anyone explain?

Thank you so much in advance!

EDIT: changed the link to point to the latest guide version (which has several typos fixed)