A Generalization of Bayesian Inference

TLDR

The paper proposes procedures that generalize Bayesian inference. It introduces probability systems that allow only bounds on event probabilities, combining sample and prior information via a specified rule. Illustrations demonstrate the approach on trinomial probabilities and monotone binomial sequences, and the paper discusses the underlying models that generate upper and lower probabilities.

Abstract

Summary Procedures of statistical inference are described which generalize Bayesian inference in specific ways. Probability is used in such a way that in general only bounds may be placed on the probabilities of given events, and probability systems of this kind are suggested both for sample information and for prior information. These systems are then combined using a specified rule. Illustrations are given for inferences about trinomial probabilities, and for inferences about a monotone sequence of binomial pi. Finally, some comments are made on the general class of models which produce upper and lower probabilities, and on the specific models which underlie the suggested inference procedures.