Thanks for the responses here’s some additional detail I should have included.
I’d like to get 2 vectors of latent traits whose posteriors are uncorrelated. I have n_respondent people each with 2 latent traits, and a set of items broken into 2 groups. By assumption trait 1 influences all items but trait 2 influences only a subset. With this structure the posterior mean correlation between factors tends to be pretty close to zero with independent normal priors or a MvNormal prior with any value of eta, but depending on the amount of data I’m fitting to there can be a fair amount of posterior density on nonzero correlations, which I want to eliminate. Here’s what that looks like with MvNormal and eta=1
By increasing eta I can concentrate the posterior more to 0 as desired, but I’m not sure if there is a better way to accomplish the same thing.