The anti-Bayesian moment and its passing

TL;DR

This paper discusses the historical and philosophical debates surrounding anti-Bayesian statements in probability theory, analyzing their origins and implications for statistical foundations.

Contribution

It provides a detailed examination of anti-Bayesian sentiments, especially Feller's extreme remarks, to clarify ongoing controversies in statistical foundations.

Findings

Analysis of Feller's anti-Bayesian statement

Historical context of anti-Bayesian remarks

Insights into ongoing statistical controversies

Abstract

The present article is the reply to the discussion of our earlier "Not only defended but also applied" (arXiv:1006.5366, to appear in The American Statistician) that arose from our memory of a particularly intemperate anti-Bayesian statement in Feller's beautiful and classic book on probability theory. We felt that it was worth exploring the very extremeness of Feller's words, along with similar anti-Bayesian remarks by others, in order to better understand the background underlying controversies that still exist regarding the foundations of statistics. We thank the four discussants of our article for their contributions to our understanding of these controversies as they have existed in the past and persist today.