Philosophy and the practice of Bayesian statistics

TL;DR

This paper challenges the philosophical view that Bayesian inference inherently supports inductive reasoning, arguing instead that it aligns better with hypothetico-deductivism and emphasizing the importance of model checking and revision.

Contribution

It clarifies the role of priors and model revision in Bayesian statistics, contrasting philosophical interpretations with practical applications and advocating for better integration of model checking.

Findings

Bayesian methods align more with hypothetico-deductivism than inductivism.

Model checking and revision are crucial in Bayesian practice but often overlooked.

Misinterpretations of Bayesian confirmation theory can hinder effective statistical practice.

Abstract

A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework.