Hi all,

Question about parameterizing a correlation/covariance matrix.

As Rick Farouni discusses here: Bayesian Factor Analysis, one way to make latent multivariate normals identifiable is to set the values for the covariance matrix N \sim (0, 1). However, this isn’t always the most interpretable prior to use.

Is there some way to create the equivalent of an orthogonal LKJ prior? My thought on the “dumb” way to do this is a separate \text{Uniform} \sim (-1, 1) for each element of the lower triangle of the correlation matrix, and then an ordered prior on the variance, however, if anyone has tried something like this before, or has thoughts, I’d be curious to hear them.

Thanks!

Adam