Posterior predictive checks

I’m still thinking about posterior predictive checks (PPC) as described in lecture notes by David Blei. I expected this to be just another device in the statistical armamentarium and was surprised to find that it’s an active area of controversy. As such, I’m not going to try to say anything definite and will just leave some bread crumbs for when I wander this way again.

The Blei notes are based largely on papers by Box (1980), Rubin (1984), and Gelman et al. (1996) (aka GMS).

PPC are discussed on Xi’an’s Og and on Gelman’s blog (and earlier). Major lines of critique are “using the data twice” and miscalibration of PPC tail probabilities when considered as frequentist *p*-values.

This also shows up in Gelman and Shalizi’s “Philosophy and the practice of Bayesian statistics” (and resulting commentary by John Kruschke).