The Bayesian Influence, or How to Sweep Subjectivism under the Carpet

Abstract

On several previous occasions I have argued the need for a Bayes/non-Bayes compromise which I regard as an application of the 'Type II' principle of rationality. By this is meant the maximization of expected utility when the labour and costs of the calculations are taken into account. Building on this theme, the present work indicates how some apparently objective statistical techniques emerge logically from subjective soil, and can be further improved if their subjective logical origins (if not always historical origins) are not ignored. There should in my opinion be a constant interplay between the subjective and objective points of view, and not a polarization separating them. Among the topics discussed are, two types of rationality, 27 'Priggish Principles', 46656 varieties of Bayesians, the Black Box theory, consistency, the unobviousness of the obvious, probabilities of events that have never occurred (namely all events), the Device of Imaginary Results, graphing the likelihoods, the hierarchy of types of probability, Type II maximum likelihood and likelihood ratio, the statistician's utilities versus the client's, the experimenter's intentions, quasi-utilities, tail-area probabilities, what is 'more extreme'?, 'deciding in advance', the harmonic mean rule of thumb for significance tests in parallel, density estimation and roughness penalties, evolving probability and pseudorandom numbers and a connection with statistical mechanics.