Hello all,
I have only just gotten my feet wet in Bayesian analysis, but I’ve read parts Kruschke’s textbook, as well as Kaplin’s Bayesian Stats for the Social Sciences. Both books emphasize how picking a prior that is conjugate to the likelihood distribution is ideal. However, for the Logistic Regression I’m currently running, the conjugate prior is the Beta distribution, which I don’t see listed in rstanarm’s priors list.
So my question is, how important is specifying the Beta distribution? How much is it going to affect the analysis in general, and my parameter estimates specifically, if I use (for example) the student t instead?
You don’t need a conjugate prior. Conjugate priors are helpful because they provide an analytical posterior, which is of real help with Gibbs sampling. With an efficient sampler as the NUTS variation implemented in Stan, there’s no real need to use a conjugate prior, so you can choose the one that best represent your prior knowledge.
Sorry to revive an old thread, but is this true? Analytic posteriors are extremely quick and I have a hard time imagining that there are no efficiency gains from using partial conjugacy.
I believe the point is that Stan does not exploit conjugacy automatically. Yes, if you work out the analytical posterior then that will typically be faster but putting a prior that happens to be conjugate shouldn’t receive any huge speed gain relative to any other prior (barring that the aforementioned prior induces bad geometry).