topic Re: PROC MCMC Bayes Factor? in Statistical Procedures

PROC MCMC Bayes Factor?

Digicha1 — Fri, 21 Feb 2025 13:23:21 GMT

Hello,

I'm trying to calculate Bayes factor (BF) from my posterior summaries from PROC MCMC. While PROC MCMC produces posterior probabilities (PP), I wondered if I could naively calculate the ratio of two of my posterior probabilities to obtain an approximate BF?

Whilst the BF is the ratio of the marginal likelihood and not the PP, if I'm assuming the same prior probabilities (no changes in prior distribution assumptions between both models), could I just take the ratio of the PP from my two models instead? I'm interested in the Bayes factor between P(Diff >0) vs P(Diff <0) in particular, so I'm planning to say BF = P(Diff >0 | D) / (P(Diff < 0 | D).

Thank you

Re: PROC MCMC Bayes Factor?

sbxkoenk — Mon, 24 Feb 2025 09:09:19 GMT

Hello,

SESUG Paper 289-2018

A Flexible Approach to Computing Bayes’ Factors with PROC MCMC

Tyler Hicks, University of Kansas

https://www.lexjansen.com/sesug/2018/SESUG2018_Paper-289_Final_PDF.pdf

Ciao, Koen

Re: PROC MCMC Bayes Factor?

Digicha1 — Mon, 24 Feb 2025 16:39:03 GMT

@sbxkoenk thanks, I found this paper too. From my understanding they have used the posterior probabilities from the outputs, whilst assuming equal prior distributions from the two hypotheses. I've assumed similarly now in my MVN model too.