Statistical Decisions Using Likelihood Information Without Prior Probabilities

This is a short 9-pp version of a longer working paper titled "Decision Making on the Sole Basis of Statistical Likelihood," School of Business Working Paper, Revised November 2004.This paper presents a decision-theoretic approach to statistical inference that satisfies the Likelihood Principle (LP) without using prior information. Unlike the Bayesian approach, which also satisfies LP, we do not assume knowledge of the prior distribution of the unknown parameter. With respect to information that can be obtained from an experiment, our solution is more efficient than Waldâ s minimax solution. However, with respect to information assumed to be known before the experiment, our solution demands less input than the Bayesian solution

Statistical decisions using likelihood information without prior probabilities

This paper presents a decision-theoretic approach to statistical inference that satisfies the Likelihood Principle (LP) without using prior information. Unlike the Bayesian approach, which also satisfies LP, we do not assume knowledge of the prior distribution of the unknown parameter. With respect to information that can be obtained from an experiment, our solution is more efficient than Wald’s minimax solution. However, with respect to information assumed to be known before the experiment, our solution demands less input than the Bayesian solution.