frequentist/Bayesian

The following is my commentary on a paper by Gelman and Robert, forthcoming (in early 2013) in the The American Statistician* (submitted October 3, 2012).

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Discussion of Gelman and Robert, “Not only defended but also applied”: The perceived absurdity of Bayesian inference”
Deborah G. Mayo

1. Introduction

I am grateful for the chance to comment on the paper by Gelman and Robert. I welcome seeing statisticians raise philosophical issues about statistical methods, and I entirely agree that methods not only should be applicable but also capable of being defended at a foundational level. “It is doubtful that even the most rabid anti-Bayesian of 2010 would claim that Bayesian inference cannot apply” (Gelman and Robert 2012, p. 6). This is clearly correct; in fact, it is not far off the mark to say that the majority of statistical applications nowadays are placed under the Bayesian umbrella, even though the goals and interpretations found there are extremely varied. There are a plethora of international societies, journals, post-docs, and prizes with “Bayesian” in their name, and a wealth of impressive new Bayesian textbooks and software is available. Even before the latest technical advances and the rise of “objective” Bayesian methods, leading statisticians were calling for eclecticism (e.g., Cox 1978), and most will claim to use a smattering of Bayesian and non-Bayesian methods, as appropriate. George Casella (to whom their paper is dedicated) and Roger Berger in their superb textbook (2002) exemplify a balanced approach. Continue reading →