Probabilistic Prediction

The posterior distribution for parameters of a data distribution is usually the major objective of a Bayesian statistical analysis. Relatively little attention has been given to the fact that either a prior or a posterior distribution implies a marginal distribution, which may be called a “predictive distribution,” for outcomes of any sample not yet observed. Predictive distributions have been mainly applied to design problems, such as determination of optimal sample size. In this paper tentative suggestions are made for applications to statistical inference, especially problems of appropriateness, selection, interpretation, and validation of formal models.