What priors are available for covariance matrices for multivariate Gaussians?

I’m curious what priors are easily available in Edward for covariance matrices? I see tensorflow has a full Wishart distribution so I assume that’s available in Edward. Also I know it is possible to make point estimates of Cholesky decompositions. I wonder if this is also feasible in a variational framework. Are there any edward examples which infer covariance matrices? I have just noticed this issue (https://github.com/blei-lab/edward/issues/471) so I’ll take a closer look at that.

Looking at the list (http://edwardlib.org/api/reference), the only distribution over positive definite matrices is the Wishart. An alternative is to appropriately transform/constrain a distribution over matrices, or build your own.

If you’re okay with point estimates, you can perform point estimation without any prior over the covariance (e.g., maximum likelihood). Simply parameterize the covariance matrix as a constrained tf.Variable. This is a common application with linear mixed models.