Bayesian issues in the 1950s: an episode involving Karl Popper and Jimmie Savage

Abstract

Abstract In the 1950s, the growing importance of Bayesian inference attracted both supporters and critics. In 1958, the philosopher Karl Popper published what he called a paradox that purported to show the foolishness of subjectivist Bayesian inference. In correspondence, Jimmie Savage pointed out what he considered an error in his reasoning, but Popper was unmoved and did not change his example when he reprinted it. It is argued that Popper did not acknowledge that the new subjectivists reasoned with distributions, not simply expected values. Excerpts from Jimmie Savage’s correspondence at the time with Popper and with Allen Wallis highlight the issues involved at this time when Bayesian statisticians were seeking general acceptance.