Philosophy and the practice of Bayesian statistics

摘要

A substantial school in the philosophy of science identifies Bayesianinference with inductive inference and even rationality as such, and seems tobe strengthened by the rise and practical success of Bayesian statistics. Weargue that the most successful forms of Bayesian statistics do not actuallysupport that particular philosophy but rather accord much better withsophisticated forms of hypothetico-deductivism. We examine the actual roleplayed by prior distributions in Bayesian models, and the crucial aspects ofmodel checking and model revision, which fall outside the scope of Bayesianconfirmation theory. We draw on the literature on the consistency of Bayesianupdating 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 encouragedresearchers to fit and compare models without checking them; at worst,theorists have actively discouraged practitioners from performing modelchecking because it does not fit into their framework.