@ssdecontrol The more I ponder your question the more it seems to be a really good question to ask about (for example, I think it speaks to something many people carry in their heads but don't generally articulate). I hope it gets more attention.

@ParagS.Chandakkar, although not written in a Bayesian context, you might be interested in reading my answer here: Multiple regression with missing predictor variable.

@Glen_b, I presume you are referring to Are prediction and distribution-fitting ever not the same thing?

@gung yes, that one.

@gung I think it's one of those sorts of questions that might benefit from some different ideas.