Why does MAP vastly outperform sample in bayesian clustering?

[iavicenna]

Thanks, I opened a new topic on this:

Mixture of Censored iid Normals

Continuing on from here: https://discourse.pymc.io/t/why-does-map-vastly-outperform-sample-in-bayesian-clustering/13190/10 where I asked about mixture of normals, thanks to @jessegrabowski and @ricardoV94, I have come to realize that due to sampling methods, in mixture models, MvNormals with diagonal cov is not identical to a bunch of univariate normals and actually can sample more efficiently (somewhat remedying label mixing if not completely). However as it stands out, MvNormals is not appl…

However a short reply, since this is MvNormal with diagonal cov normally, its pdf would actually be just a product of two independent normals which could in theory be censored independently. Not sure how to implement it though and if possible by still keeping the non-mixing property of the MvNormal.