The Assessment of Prior Distributions in Bayesian Analysis

Abstract

In the Bayesian framework, quantified judgments about uncertainty are an indispensable input to methods of statistical inference and decision. Ultimately, all components of the formal mathematical models underlying inferential procedures represent quantified judgments. In this study, the focus is on just one component, the prior distribution, and on some of the problems of assessment that arise when a person tries to express prior distributions in quantitative form. The objective is to point toward assessment procedures that can actually be used. One particular type of statistical problem is considered and several techniques of assessment are presented, together with the necessary instruction so that these techniques can be understood and applied. A questionnaire is developed and used in a study in which people actually assess prior distributions. The results indicate that, by and large, it is feasible to question people about subjective prior probability distributions, although this depends on the assessor and on the assessment technique(s) used. A revised questionnaire, which is aimed at potential users of the assessment procedures and future investigators in the area of probability assessment, is presented.