Fisher, Jeffreys, and the Nature of Probability

Abstract

Bayesian inference was Fisher’s intellectual bête noire. His work is filled with sharp attacks on “inverse probability”,¹ and for many years he sought to develop a logic of induction alternative to the Bayesian scheme. In this connection he developed some of his central ideas, including the likelihood-based theory of estimation and the theory of fiducial probability. This lecture is about Fisher’s critique of Bayesian inference. It centers on an acerbic and amusing exchange between Fisher and Jeffreys which took place in the 1930s and revealed which parts of the Bayesian theory Fisher rejected, and which parts he simply failed to comprehend. First, I shall briefly summarize two papers on inverse probability which antedate this exchange, and at the end of the lecture I shall mention a few later changes in point of view which brought Fisher more into line with the ideas argued by Jeffreys in their exchange — but which Fisher had rejected out of hand at the time.