Practicals of Uncertainty [book review]

On my way to the O’Bayes 2017 conference in Austin, I [paradoxically!] went through Jay Kadane’s Pragmatics of Uncertainty, which had been published earlier this year by CRC Press. The book is to be seen as a practical illustration of the Principles of Uncertainty Jay wrote in 2011 (and I reviewed for CHANCE). The avowed purpose is to allow the reader to check through Jay’s applied work whether or not he had “made good” on setting out clearly the motivations for his subjective Bayesian modelling. (While I presume the use of the same P of U in both books is mostly a coincidence, I started wondering how a third P of U volume could be called. Perils of Uncertainty? Peddlers of Uncertainty? The game is afoot!)

The structure of the book is a collection of fifteen case studies undertaken by Jay over the past 30 years, covering paleontology, survey sampling, legal expertises, physics, climate, and even medieval Norwegian history. Each chapter starts with a short introduction that often explains how he came by the problem (most often as an interesting PhD student consulting project at CMU), what were the difficulties in the analysis, and what became of his co-authors. As noted by the author, the main bulk of each chapter is the reprint (in a unified style) of the paper and most of these papers are actually and freely available on-line. The chapter always concludes with an epilogue (or post-mortem) that re-considers (very briefly) what had been done and what could have been done and whether or not the Bayesian perspective was useful for the problem (unsurprisingly so for the majority of the chapters!). There are also reading suggestions in the other P of U and a few exercises.

“The purpose of the book is philosophical, to address, with specific examples, the question of whether Bayesian statistics is ready for prime time. Can it be used in a variety of applied settings to address real applied problems?”

The book thus comes as a logical complement of the Principles, to demonstrate how Jay himself did apply his Bayesian principles to specific cases and how one can set the construction of a prior, of a loss function or of a statistical model in identifiable parts that can then be criticised or reanalysed. I find browsing through this series of fourteen different problems fascinating and exhilarating, while I admire the dedication of Jay to every case he presents in the book. I also feel that this comes as a perfect complement to the earlier P of U, in that it makes refering to a complete application of a given principle most straightforward, the problem being entirely described, analysed, and in most cases solved within a given chapter. A few chapters have discussions, being published in the Valencia meeting proceedings or another journal with discussions.

While all papers have been reset in the book style, I wish the graphs had been edited as well as they do not always look pretty. Although this would have implied a massive effort, it would have also been great had each chapter and problem been re-analysed or at least discussed by another fellow (?!) Bayesian in order to illustrate the impact of individual modelling sensibilities. This may however be a future project for a graduate class. Assuming all datasets are available, which is unclear from the text.

“We think however that Bayes factors are overemphasized. In the very special case in which there are only two possible “states of the world”, Bayes factors are sufficient. However in the typical case in which there are many possible states of the world, Bayes factors are sufficient only when the decision-maker’s loss has only two values.” (p. 278)

The above is in Jay’s reply to a comment from John Skilling regretting the absence of marginal likelihoods in the chapter. Reply to which I completely subscribe.

[Usual warning: this review should find its way into CHANCE book reviews at some point, with a fairly similar content.]