On the Empirical Validity of the Bayesian Method

Abstract

SUMMARY The ideas in Kolmogorov's programme for algorithmic substantiation of applications of probability make it possible to define a measure of disagreement between the probability distribution representing the attitude of a coherent individual towards a random experiment and the outcome of the experiment. When there is agreement we say that the probability distribution is empirically valid. We prove quantitatively that formulae of Bayesian statistics transform empirically valid probability distributions into other empirically valid distributions.