On Prior Distributions for Binary Trials

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.