Dear,

I wonder how I can exactly enforce independence on two vectors within the same matrix. Imagine matrix f with two columns and 20 rows. Each element in f is a parameter of which I can assume normal distribution. I want to enforce as little covariance between the two columns as possible and preferably each of them to have a variance of one. What would this look like?

\begin{pmatrix} f[,1]\\ f[,2] \end{pmatrix} \sim mvn \begin{pmatrix} 0\\ 0 \end{pmatrix} , \begin{pmatrix} 1 & 0\\ 0 & 1 \end{pmatrix}

```
// code 1
parameters{
matrix[20, 2] f;
}
transformed parameters{
vector[20] zeros;
matrix[20,20] Sigma;
zeros = rep_vector(0, 20);
Sigma = diag_matrix(rep_vector(1, 20));
}
model{
for(p in 1:2) f[p] ~ multi_norm( zeros, Sigma);
}
```

Or alternatively:

```
// code 2
parameters{
matrix[20, 2] f;
}
transformed parameters{
vector[2] zeros;
matrix[2, 2] Sigma;
zeros = rep_vector(0, 2);
Sigma = diag_matrix( rep_vector(1, 2));
}
model{
for(i in 1:20) f[i] ~ multi_norm( zeros, Sigma);
}
```

Should one of these do it? I have been getting some mixed results that make me doubt if I’m coding this correctly.

Thank you!