I had a brief chat with Andrew Gelman about the topic of generative vs. discriminative models. It came up when I was asking him why he didn’t like the frequentist semicolon notation for variables that are not random. He said that in Bayesian analyses, all the variables are considered random. It just turns out we can sidestep having to model the predictors (i.e., covariates or features) in a regression. Andrew explains how this works in section 14.1, subsection “Formal Bayesian justification of conditional modeling” in Bayesian Data Analysis, 2nd Edition (the 3rd Edition is now complete and will be out in the foreseeable future). I’ll repeat the argument here.