Bayesian Analysis for Binomial Models with Generalized Beta Prior Distributions

Abstract

The Libby-Novick class of three-parameter generalized beta distributions is shown to provide a rich class of prior distributions for the binomial model that removes some of the restrictions of the standard beta class. The posterior distribution defines a new class of four-parameter generalized beta distributions for which numerical posterior analysis is easily done. A numerical example indicates the desirability of using these wider classes of densities for binomial models, particularly in an interactive computing environment.