The Likelihood Principle

Abstract

The likelihood principle (LP) is a normative principle for evaluating statistical inference procedures. The LP can be proved from arguably self-evident premises; indeed, it can be proved to be logically equivalent to these premises. This chapter attempts to prove a precise version of the LP, with a number of caveats; and briefly mentions some alternative versions. The importance of the likelihood principle is that it discusses if the comparison is not relevant. LP does rule out many specific inferences. It allows categorizing methods of statistical inference in a very natural and powerful way: a way, which is more abstract and more general than the usual ways of classifying statistical theories. The LP also captures some of the most attractive features of Bayesianism, while leaving open the question of whether a subjective prior should be. Since it provides a lot of common ground between factions of Bayesians, the LP is a good, irenic starting point for agreement between factions of philosophers of statistics.