"Not only defended but also applied": The perceived absurdity of Bayesian inference

TL;DR

This paper examines the misconceptions and criticisms of Bayesian inference, analyzing historical and recent examples to understand why some consider Bayesian methods absurd or misguided.

Contribution

It provides a nuanced analysis of the misconceptions surrounding Bayesian inference, clarifying the intellectual background behind these criticisms.

Findings

Identifies historical misconceptions about Bayesian methods

Analyzes recent criticisms like the doomsday argument

Clarifies the philosophical misunderstandings of Bayesian inference

Abstract

The missionary zeal of many Bayesians of old has been matched, in the other direction, by a view among some theoreticians that Bayesian methods are absurd-not merely misguided but obviously wrong in principle. We consider several examples, beginning with Feller's classic text on probability theory and continuing with more recent cases such as the perceived Bayesian nature of the so-called doomsday argument. We analyze in this note the intellectual background behind various misconceptions about Bayesian statistics, without aiming at a complete historical coverage of the reasons for this dismissal.