Jaynes’ re-read

Following the two past PhD courses on Jeffreys‘ Theory of Probability and Keynes‘ Treatise On Probability, I will propose next year a reading course at CREST on Jaynes’s Probability Theory.

Jeffreys and Jaynes share a lot in common as physicists who both significantly contributed to Bayesian statistical theory and as writers of books with almost identical titles and with very ambitious and similar scopes. It is thus no surprise that Jaynes dedicates his book to Jeffreys. There are also differences, the most obvious one being that Jeffreys published his foundational book before his 50th birthday, while Jaynes’ book came out more than ten years after his death (under the scholarly supervision of Larry Bretthorst). The time difference between both books is not that revelant, however, in that Jaynes’s Probability Theory is what Persi Diaconis call “wonderfully out of date” in his review. (Meaning “Jaynes’s focus on basic philosophical issues [rather than on computational techniques] is timeless“, with the conclusion that  “this is the best introduction to Bayesian statistics that I know”!)

I plan to cover in the lectures what I consider to be the most significant aspects of Jaynes’s work. The corpus of work corresponding to the logical foundations of probability theory and the opposition of Jaynes to (Feller’s) measure theory, Bourbakism, Kolmogorov’s axioms, (Feller’s) countable additivity, de Finetti’s principles, and other probabilistic paradoxes will not be adressed, even though a second course by a probabilist colleague of mine at Dauphine may follow this one. The lectures will focus on

1. the meaning and motivation of prior distributions (Chapter 6), culminating in the definition of the entropy principle (Chapter 11)
2. the rules of hypothesis testing (Chapter 4) and the central role of evidence (Chapters 9 and 18)
3. the special case of transformation groups (Chapter 12) and the debate about marginalisation paradoxes (Chapter 15)
4. Bayesian estimation (Chapter 6) and the criticisms on decision theory (Chapters 13 and 14)
5. Model comparison (Chapter 20) and the pathologies of orthodox methods (Chapters 16 and 17)

The dates of the course are already set: March 21, 24, 28, 31 and April 04 [2011]…