Frequentist-leaning statisticians have numerous responses to Bayesian criticisms that may not be widely known. Broadly speaking, these rebuttals assert that Bayesian criticisms of Frequentist approaches rely on circular arguments, are self-refuting, rest mostly on semantics, or are mainly of interest to academics and irrelevant in practice. Below, I've briefly summarized the ones I'm aware of from memory and in my own words. The meaning of the term is often unclear. Is it objective Bayes, subjective Bayes, approximate Bayes, empirical Bayes, or all of the above?

I happened to recently reread this article of mine from 2010, and I absolutely love it. I don't think it's been read by many people--it was published as one of three discussions of an article by Brad Efron in Statistical Science--so I wanted to share it with you again here. The information principle: the key to a good statistical method is not its underlying philosophy or mathematical reasoning, but rather what information the method allows us to use. Good methods make use of more information. The methodological attribution problem: the many useful contributions of a good statistical consultant, or collaborator, will often be attributed to the statistician's methods or philosophy rather than to the artful efforts of the statistician himself or herself.