I’ve been reading a bunch of papers on Bayesian statistical inference lately, somewhat to my regret. I have no particular objection to Bayesian statistics, but distressingly often, a Bayesian paper will include a gratuitous slam of all other types of statistics. D. V. Lindley’s papers (which are classics in the literature) are particularly noxious in this regard. It’s a strange pattern, and I’d be curious to know the history of the habit.
More pleasant is a paper by Brad Efron based on an address he gave at Phystat2003, Bayesians, Frequentists, and Physics, which offers a detente in the Bayesian-frequentist debate. He describes Stein’s paradox, which is a challenge from both the Bayesian and classical points of view, and discusses means of inference, such as empirical Bayes, which are (arguably) neither purely Bayesian nor purely frequentist.