Principles of Uncertainty (Second Edition)

Abstract

A new edition of Principles of Uncertainty, the first edition of which I reviewed in JASA (2012), has appeared. I was asked by CRC Press to review the new book; here are some (almost raw) extracts from my report, removing the parts that were addressed by the author before the book went to print. Overall, my enthusiasm for the book, its original (and of course, subjective) defense of the Bayesian approach, and its highly enjoyable style, remains intact, especially when backed by the proof-in-the pudding 2017 Pragmatics of Uncertainty, which I reviewed in a 2019 issue of CHANCE (32(1)). In Chapter 6, the proof of the Central Limit Theorem uses the “smudge” technique, which is to add an independent noise to both the sequence of rvs and its limit. This is most effective and reminds me of quite a similar proof Jacques Neveu used in probability notes at the École Polytechnique, which went under the more-formal denomination of convolution, with the same (commendable) purpose of avoiding Fourier transforms. If anything, I would have favored a slightly more-condensed presentation in fewer than eight pages. In Chapter 7, I found a nice mention of (Hermann) Rubin’s insistence on not separating probability and utility because only the product matters. And another fascinating quote from Keynes, not from his early statistician years, but in 1937 as an established economist: