Multivariate Normal Distribution Diagonal Covariance Matrix

Question

I am reading through a paper and they have a multivariate distribution with the second parameter (covariance matrix as follows)

I know its hard to determine without context but what does this imply (covariance matrix = sI) ? None of the variables are related?

Answer 1

This means "multivariate normal" with (vector) mean ${\bf m}^0$ and covariance scalar $s^0$ times the identity matrix, ${\bf I}$.