Finding the Bayes factor using Stan

[dhanur88]

Hi everyone,

I want to calculate the Bayes factor to do some hypothesis testing for the models that I am fitting using Stan. But based on this post, calculating Bayes factor directly using rstan seems to be not a straight forward thing.

Calculating Bayes Factor using Stan

Hello Stan Community! As we are all aware that, Stan gives an estimate of the log marginal likelihood (lp__) in the output along with the estimates of the other parameters. My question is, can I use this estimate of lp__ to calculate Bayes Factors (exp(lp__Null - lp__Alternative) ? Any help is much appreciated! Thank you!

Also I have seen several posts regarding calculating the Bayes factor using some packages like brms, rstanarm which directly use Stan.

So will it be possible to find the Bayes factor directly using Stan?
Because I may need to rely on Stan directly to fit models rather than using some built in packages.

Any suggestion will be highly helpful. Thank you.

[hhau]

@dhanur88

brms , rstanarm which directly use Stan

I think both of these packages use bridgesampling, and I suggest you do too :).

[dhanur88]

@hhau Thank you for the suggestion. So is it possible to use Stan and bridgesampling package together(may be something like using the Stan objects inside bridgesampling)? Because I may need to use Stan for modelling.

[Stephen_Martin]

Yes, you can.
You just need to use the unnormalized probability functions (e.g., use target += normal_lpdf(theta | 0, 1) instead of theta ~ normal(0,1)).

Depending on your model comparison or hypothesis testing goals, you may also be able to use the savage-dickey method, but bridgesampling is more general.

[hhau]

There is a vignette on precisely this topic: https://cran.r-project.org/web/packages/bridgesampling/vignettes/bridgesampling_example_stan.html