Keynes among the Statisticians

Reading Keynes' Treatise on Probability

“…This lack of innovative material, along with the harsh tone of a critic who had contributed so little to the field, may explain why Keynes' incursion in probability and statistics did not have a lasting impact, since even those most sympathetic to the book (Jeffreys, 1931; Lindley, 1968) saw no practical nor methodological aspect to draw from and praised aspects external to their own field (Aldrich, 2008a). Stigler (2002, pp.…”

“…After an extensive criticism of the methods of the time and of the use of mathematical models as a basis for statistical inference (see ), Keynes concludes the Treatise with a defence of the method advocated by the late Lexis (who died in 1914), at the very moment Fisher (1925) was defining statistics as “mathematics applied to data”. As analysed by Aldrich (2008, ), the defence is paired with Keynes’ attempt to link Lexis’ theory to his own principles of analogy in induction, as advanced in Part III of the Treatise . The following quote indicates why the attempt failed.…”

“…Before engaging upon this review, we point out that the Treatise has been previously assessed by Stigler (2002), who was similarly critical on the depth of the book, and by Aldrich (2008a), who produced an extensive and scholarly survey on the impact (or lack thereof) of Keynes on the philosophical and statistical communities at the time. The later includes in particular a detailed study of the reviews written on A Treatise on Probability by philosophers and statisticians of the early 20th century, including Fisher (1923) and Jeffreys (1931).…”

“…Aldrich (2008a) argues quite convincingly that these are maximum a posteriori (MAP) estimates corresponding to flat priors, making the term most probable more coherent. When stating the problem on p. 194, Keynes indeed invokes the “theorem of inverse probability”, namely Bayes’ theorem on the parameter finite set.…”

“…1 1 It is worth pointing out that the denomination of ‘Bayesian’ appeared much later (Fienberg 2006), Keynes resorting to the (then) current denomination of Inverse Probability or, in a more derogatory way, “the Laplacian theory of ‘unknown probabilities” (p. 372). Referring to the authoritative arguments of Aldrich (2008a), we stress that the papers of Keynes on statistics were definitely Bayesian with most of his analysis being based on an uniform prior. He later started to worry about the influence of the prior, leading to the Treatise and to its harsh criticism of inverse probability, even though some Bayesian arguments remain in use within the book (see Note 4).…”