Coherent predictive probabilities

Abstract

The main aim of this thesis is to study ways of predicting the outcome of a vector of category counts from a particular group, in the presence of like data from other groups regarded exchangeably with this one and with each other. The situation is formulated using the subjectivist framework and strategies for estimating these predictive probabilities are presented and analysed with regard to their coherency. The range of estimation procedures considered covers naive, empirical Bayes and hierarchical Bayesian methods. Surprisingly, it turns out that some of these strategies must be asserted with zero probability of being used, in order for them to be coherent. A theory is developed which proves to be very useful in determining whether or not this is the case for a given collection of predictive probabilities. The conclusion is that truly Bayesian inference may lie behind all of the coherent strategies discovered, even when they are proposed under the guise of some other motivation.