## le bayésianisme aujourd’hui [book review]

**I**t is quite rare to see a book published in French about Bayesian statistics and even rarer to find one that connects philosophy of science, foundations of probability, statistics, and applications in neurosciences and artificial intelligence. Le bayésianisme aujourd’hui (Bayesianism today) was edited by Isabelle Drouet, a Reader in Philosophy at La Sorbonne. And includes a chapter of mine on the basics of Bayesian inference (à la Bayesian Choice), written in French like the rest of the book.

The title of the book is rather surprising (to me) as I had never heard the term Bayesianism mentioned before. As shown by this link, the term apparently exists. (Even though I dislike the sound of it!) The notion is one of a probabilistic structure of knowledge and learning, à la Poincaré. As described in the beginning of the book. But I fear the arguments minimising the subjectivity of the Bayesian approach should not be advanced, following my new stance on the relativity of probabilistic statements, if only because they are defensive and open the path all too easily to counterarguments. Similarly, the argument according to which the “Big Data” era makesp the impact of the prior negligible and paradoxically justifies the use of Bayesian methods is limited to the case of little Big Data, i.e., when the observations are more or less iid with a limited number of parameters. Not when the number of parameters explodes. Another set of arguments that I find both more modern and compelling [for being modern is not necessarily a plus!] is the ease with which the Bayesian framework allows for integrative and cooperative learning. Along with its ultimate modularity, since each component of the learning mechanism can be extracted and replaced with an alternative.

One of the first chapters in the book by B. Ossimani and F. Russo covers objective Bayesian methods as a precautionary principle. However, perceiving Jaynes‘ maximum entropy principle as an objective principle is limited to discrete settings. For the well-known—if ignored there—difficulty of the reference measure in the continuous case. The chapter also mentions Jon Williamson, whose Defense of Objective Bayesianism I was unaware of. (Both authors of the chapter are co-authors of Williamson.) The opposition between “the” objective and “the” empirical Bayes approach strike me there as being restricted to formal settings, for uniqueness to hold. The following chapters in the first part are devoted to expert systems and game theory. The following chapter is more surprising [for me] as it deals with social epistemology. This does not mean anything to me, but, reading through it, it appears as a theory of aggregating posteriors. Which was an interesting question until I read the setting is restricted to a finite probability space! Because, in the continuous case, the measures could be conflicting, i.e., not being all absolutely continuous against the same measure. Which would lead to an exciting debate on how to make the different objects communicate if not agree.

The second part is on the Bayesian approach in statistics *[with a typo in the title confounding statistics as a field and statistics as a collection of figures]*. The first chapter by Jan Sprenger centres on the notion of evidence, addressing more the issues with the p-values than the calibration of the Bayes factor, somewhat hitting the wall on that point. In a second and connected chapter, Bruno Lecoutre recalls the historical developments of the approaches of Jeffreys, Fisher, and Neyman and Pearson, with a critical perspective on the decision side of testing (and our own reassessment).

The last part of the book covers the description and motivation of a Bayesian approach in various fields: food security, climate, population genetics, metrology (which reminded me of the meeting I attended last year), neurosciences, cognition, and medical diagnostics. With a repeated attention to the interpretation(s) of the posterior distribution, from a pure frequentist vision to epistemist, metaphysical, and even social apprehensions. I actually found this section the most interesting part of the book in that the authors brought in and explained their experience and motivations in constructing prior distributions and representing uncertainty. While the whole enterprise (represented by this book) is definitely worthwhile, from aggregating many viewpoints on the Bayesian approach to scientific reasoning, to surveying the (mostly) recent literature on the evolution of this Bayesian perspective, to illustrating actual practices in conducting Bayesian inference, and to demonstrating a lively “French scene” in this domain (a clear change from the 1980’s!), I presume too many books with a similar content can be found in English to call for a translation.

## Leave a Reply