Compromising Bayesianism: a plea for indeterminacy

Abstract

Jack Good reports in one of his papers that in 1947 he had a nonmonetary bet with M.S. Bartlett that the predominant philosophy of statistics one century later would be Bayesian. By 1979, Good modified his forecast. He then suggested that the predominant philosophy of statistics would be a Bayes-non-Bayes synthesis or compromise (Good, 1979). presumably the basis both for the original forecast and its updated revision had less to do with extrapolations from trends then discernible in the thinking of his colleagues than with his optimistic assessment that Good thinking is the wave of the future together with his privileged relation to the source of this inspiration. Good’s predictions appear to be borne out to a considerable degree. Bayesianism has not silenced its critics among statisticians or philosophers who think about probability, induction and statistics. Still the contrast between the status of Bayesian ideas in the 1940’s and now is astounding. More interesting yet, however, is the fact that even as the friends of Bayesianism multiply, there is also growing sympathy for ideas which are reminiscent of what Jack seems to have in mind by a Bayes-nonBayes compromise. Perhaps the major impetus for Good’s quest for Bayes-non-Bayes compromises derives from the extremely demanding character of Bayesian ideals of rational belief, valuation and choice when it comes to applications. We cannot be expected to represent our probability assignments to hypotheses by precisely specified real numbers. The same applies to our utility judgements. Furthermore, Bayesian modelling of realistic situations often requires a complexity of structure which renders solutions to statistical decision problems difficult because of the costs of computation and, indeed, often because of the lack of computational techniques for any price. Worshippers in the Bayesian temple must, perforce, compromise the principles of the true church when facing the real world. Good was always sensitive to this point. Even when he was one of the lonely voices speaking out for a Bayesian point of view, he was thinking about ways and means to address questions about the application of Bayesian ideals. His discussions