Chapter 6 - Priors

Abstract

This chapter deals with use of priors in Bayesian inference. The philosophical appeal of Bayesian inference—its coherent use of probability to quantify all uncertainty, its simplicity, and exactness—all of this is set at nought for some by the necessity of specifying priors for unknown parameters. The subjectivity associated with choosing priors is the biggest barrier to the widespread use of Bayesian inference methods by scientists today. Prior knowledge of a parameter, whether from previous studies or informed common sense, might be quantified in terms of a probability distribution. This distribution is described as an “informative” prior. Posterior inference is the formal mechanism for incorporating prior knowledge with the information provided by data. Many solutions of possible noninformative priors have been offered to the question of how one is to produce an objective Bayesian analysis, one which removes the taint of subjectivity or arbitrariness from the process of inference, such as uniform priors, priors based on conjugacy, and Jeffreys priors.