I would be very interested in seeing how you implemented the hierarchical PPCA.
My problem was that I couldn't identify the coefficients. So for instance, the first principal component could be [x, x, x, ...] or [-x, -x, -x, ...] and the result would be some bimodal distribution. So if you placed restrictions on the first PC it would work (like only positive), but those restrictions may not make sense for the next PCs.
Yes, multimodality is often a problem for mcmc clustering or dimensionality reduction. However, if you use the SVD method to estimate PCA you only have a bimodal distribution since SVD is identified up to the sign. Asymmetric initialization is usually enough to solve the problem.
My problem was that I couldn't identify the coefficients. So for instance, the first principal component could be [x, x, x, ...] or [-x, -x, -x, ...] and the result would be some bimodal distribution. So if you placed restrictions on the first PC it would work (like only positive), but those restrictions may not make sense for the next PCs.