Bayesian Confirmation Theory and The Likelihood Principle

Abstract

The likelihood principle (LP) is a core issue in disagreements between Bayesian and frequentist statistical theories. Yet statements of the LP are often ambiguous, while arguments for why a Bayesian must accept it rely upon unexamined implicit premises. I distinguish two propositions associated with the LP, which I label LP1 and LP2. I maintain that there is a compelling Bayesian argument for LP1, based upon strict conditionalization, standard Bayesian decision theory, and a proposition I call the practical relevance principle. In contrast, I argue that there is no similarly compelling argument for or against LP2. I suggest that these conclusions lead to a restrictedly pluralistic view of Bayesian confirmation measures.