Dear Pyro-Forum,

I am trying to implement a multivariate Normal prior over columns of a matrix with different covariance matrices for each column, i.e. for matrix A we have a_.,j as individual columns of A and a_.,j ~ N(0, Sigma_j), for j=1,…,R.

I have tried a sequential plate statement:

```
core_a = torch.empty(self.output_dim, self.rank)
core_b = torch.empty(self.feature_dim, self.rank)
for j in pyro.plate(name='rank_dim', size=self.rank):
core_a[:, j] = pyro.sample(name='column_a_{}'.format(j),
fn=dist.MultivariateNormal(loc=torch.zeros(self.output_dim),
covariance_matrix=cov_core_a[:, :, j]))
```

However, the AutoGuide I am currently using does not support sequential plates.

Does anyone have a suggestion how to vectorize this kind of prior?

Best Regrads!