The Most Conservative Beta Prior Distribution for Binomial Sampling

Abstract

**Please note that the full text is embargoed** ABSTRACT: The incorporation of prior information about a parameter into a statistical procedure is an essential feature of Bayesian statistics. However, the manner in which this is done is often arbitrary. In order to reduce such arbitrariness, methodology based on information theoretic concepts is introduced which (a) quantifies the amount of information provided by the sample data relative to that provided by the prior distribution and (b) allows for a ranking of prior distributions with respect to conservativeness, where conservatism refers to restraint of extraneous information which is embedded in any prior distribution of the parameter. To illustrate the implementation of the methodology, the most conservative beta prior distribution under a binomial sampling model is determined for three situations: (1) no prior estimate of ^, where ^ is the success probability, is available, (2) a prior point estimate of ^ is available, and (3) a prior interval estimate of ^ is available.