The Assessment of Prior Distributions in Bayesian Analysis

TLDR

In Bayesian inference, all model components are quantified judgments about uncertainty, making such judgments indispensable to statistical inference. The study aims to identify practical assessment procedures for prior distributions in Bayesian analysis. The authors examine a specific statistical problem, present several assessment techniques with instructions, develop and administer a questionnaire to evaluate how people assess prior distributions, and provide a revised questionnaire for future users. The results show that questioning people about subjective prior distributions is largely feasible, though effectiveness varies with the assessor and the assessment technique.

Abstract

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.