Why is the Bayes Factor Package so fast?
I have been doing some testing trying to get rstanarm results to somewhat match BayesFactor results (matching the default cauchy prior etc), just for my own understanding. Also, I need to do logistic regression and can't yet with the BayesFactor package so I would rely on rstanarm or BRMS.
This is probably well known and very silly question and I feel stupid asking but why is the BayesFactor package so fast compared to BRMS and co? I know BRMS and STAN and co uses MCMC, so sampling can take a long time (and get way too long for some of the models I need). If not sampling, what is happening under the hood of the BayesFactor package? I am assuming some kind of approximation? Will this kind of speed eventually be workable with logistic mixed models etc?
Is this possible to understand in laymen's terms?
Comments
I am not 100% certain, but I think BayesFactor integrates out the random effects, such that the key measure of interest requires only a one-dimensional integral. When you add particular effects to the ANOVA model (which cannot be integrated out) the estimation slows down considerably.
Cheers,
E.J.