The 1988 Wald Memorial Lectures: The Present Position in Bayesian Statistics

摘要: The first five sections of the paper describe Bayesian paradigm for statistics and its relationship with other attitudes towards inference. Section 1 outlines Wald's major contributions explains how they omit vital consideration coherence. When this point is included view results, main difference that Waldean ideas require concept sample space, whereas approach may dispense it, using a probability distribution over parameter space instead. 2 relates statistical to problem inference in science. Scientific essentially passage from observed, past data unobserved, future data. roles models theories doing are explored. all should be accomplished entirely within calculus 3 justifies choice by various axiom systems. claim made leads quite different classical and, particular, prob- lems latter cease have importance other. Point estimation provides an illustration. Some counter-examples discussed. It important conclusions usable making decisions. 4 achieves practi- cality introducing utilities principle maximizing expected utility. Practitioners often unhappy basing inferences on one number, probability, or action another, expectation, so these points considered methods justified. 5 discusses why viewpoint has not achieved success logic suggests. Points discussed include between practical situation, example multiple comparisons; lack need confine attention normality exponential family. Its extensive use nonstatisticians documented. most objection which rightly says probabilities hard assess. Consequently 6 considers might done attempt appreciate accurate formulae like extension conversation, product law Bayes rule evaluating probabilities.