## Bayesian Decision Analysis

**I**n 1989, I wrote my very first book review, which appeared in JASA, about “*Decision Analysis: A Bayesian Approach*“, by J.Q. Smith, professor at the University of Warwick. I have now received from the Short Book Reviews section of the International Statistical Review another book of Jim Smith to review, namely ** Bayesian Decision Analysis**. Before getting on discussing the current book, let me acknowledge that my review of 1989 was far too rash and critical! While acknowledging that the 1989 book developed “concepts not usually dealt with in Bayesian classics”, I bemoaned the lack of connections with classical Bayesian decision theory, as exemplified by Berger (1985) and missing entries about noninformative priors, prior construction, bounded loss shortcomings, &tc. While I remain attached to the approach adopted in Jim [Berger]’s book, I now see much more clearly the point made in Jim [Smith]’s 1989 book and thus regret

*a posteriori*the tone of this review as

*une erreur de jeunesse*…

“Bayesian inference is a rather different discipline from Bayesian decision analysis. [It] will typically focus on the logical implication of a particular set of experiments on inferences about the generating process of that particular dataset once it has been seen.”Bayesian Decision Analysis, page 132.

If we now move twenty years forward and consider ** Bayesian Decision Analysis**, the book somehow covers the same ground [as the 1989 book] of Bayesian decision analysis, as opposed to Bayesian inference, but a deeper and more mature level. Jim Smith has been involved quite a lot in consulting experiences, in particular in connection with nuclear energy (hence the link on the cover), and the expertise he gained from such experiences shows throughout the book. It mostly skips the traditional Bayesian inference with its use of parameterised models. Hence a logical lack of entry on computational aspects and on hierarchical models, except for Chapter 9, for Jim Smith considers tree models to be superior to the later, both in terms of versatility and of symmetries. Before moving to a brief description of the chapters, let me stress that the design and the printing of the book are both of the highest quality, numerous tree graphs appearing seamlessly at the right place [making captions superfluous], different fonts making parts more coherent and so on. [The product is so nice that my neighbours in the métro looked at me reproachfully each time I was writing a comment in the margin!] I spotted very few typos and I must only mention the one massacring Maurice Allais’ name into Allias (!), if only because he is an alumni of my kids’ school. (I must also point out to Jim that my own book is called

**, not**

*The Bayesian Choice**The Bayesian Case*!, even though it could have worked as a title…) [It looks as is the file was recomposed by CUP as otherwise a typo turning a β into a 3 (page 77) would not make any sense.]

*“Effective decision analysis is intrinsically subjective.” ** ***Bayesian Decision Analysis***, page 320.*

**T**he introduction of ** Bayesian Decision Analysis** is very good if only because it avoids to jump into a mathematisation of the issues by sticking to a few coherent if classic examples. It stresses the fundamental difference with Bayesian inference from Section 1.0.2, namely that “Bayesian decision analysis is focused on solving a given problem.” [I wish I had not missed this point in 1989…] The second chapter is a wonderful entry on trees, making their construction and the resulting optimal decision quite intuitive. Although this is short from impossible, I would have liked a more realistic worked-out example [but this would have clearly dwarfed the current size of the book!]. This chapter also reminded me of the very enjoyable 1968 book by Raiffa… Chapter 3 on utilities and rewards feels more traditional, a wee à la DeGroot, with a well-argumented introduction of loos functions via a system of rational axioms. The following chapter on subjective probability [and its] elicitation actually steps away from classical textbooks by focussing on the finite universes covered by decision trees [an opportunity to point out the very nice distinction between analyst, decision maker, expert and auditor, if not the annoying gender game played with those!]. The final chapter of the first part on Bayesian inference is maybe less necessary, even I appreciate [of course] the part about mixtures, as well as the final section on the role of Bayesian inference in decision analysis [incl. counterfactuals].

*“If I am not going to received the reward of spending time with [my partner], I find being in the the bar more preferable that being at home alone” ** ***Bayesian Decision Analysis***, page 132.*

**T**he second part starts with a hugely interesting chapter about multiple attribute utility theory, incl. an almost real-life Chernobyl illustration. The most developed case is obviously the additive type of utility function, but this seems almost unavoidable in real-life settings. [I love the above quote with the typo, wondering whether or not Jim wrote it when back from the bar!] Chapter 7 covers DAGSs in a Lauritzen-ian way, but also the elicitation of a Bayesian network in an almost-practical way (using a pipeline case as a reference example). The next chapter is about influence diagrams and causality, i.e. when prior modelling meets utility, connecting with earlier books of Shafer and Pearl. Chapter 9 on multidimensional learning covers inference on probabilities in Bayesian networks, while the final chapter very nicely and honestly summarises the strengths and difficulties of Bayesian decision analysis. I thus hope it is obvious I strongly recommend reading the book to all involved in any level of decision management! Or teaching it. [A companion case studies book would be nice too!]

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