On Prior Distributions for Binary Trials

Abstract

Although there are basically two models for binary trials—a parametric model and an observabilistic or predictive model—for purposes of inference the former can be considered a special or limiting case of the latter. This being so, when little is known or it is desired to adopt an impartial stance about the object of inference before conducting a series of binary trials, applying a Bayesian approach to the predictive case is shown to suffice for the parametric case as well. It is argued that the prior distribution judged reasonable in the observabilistic case implies a prior distribution for the parametric case that is more compelling than others derived especially for the latter. This prior is, incidentally, attributed to Bayes and Laplace.

Key Words:

• Bayesian inference
• Binary trials
• Likelihood principle
• Noninformative
• Predictivism
• Prior distributions