Is there a Mathematica package for Bayesian linear regression?
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There is a lot around:
I am a bit late, but here is a short paper of mine with Wolfram Language code. It covers Bayesian regression as well as model selection. Take notice of the books in the references. Excellent for self study. http://djafari.free.fr/MaxEnt2014/papers/04_paper.pdf
For some reason this question didn't come up when I tried searching for it before, so I ended up creating a new question for it and answering it myself.
In this answer I provide a link to my Bayesian inference repository which has a function that's the Bayesian equivalent of Mathematica's