Approximately Bayesian Inference

Abstract

Consider statistical inference about a scalar parameter and suppose that information about that parameter is to be summarized by a system of interval estimates. It is well known that methods of interval estimation that do not correspond to Bayesian inference with respect to some prior distribution have some logical difficulties. This article proposes a measure of how close a system of interval estimates is to being of Bayesian form. Using this measure, several non-Bayesian methods of interval estimation are analyzed; these results are illustrated on several examples.

Key Words:

• Asymptotic theory
• Conditional inference
• Interval estimation
• Likelihood inference