I just learned that Paul Deheuvels died last week. He was head of the statistics department at Université Pierre & Marie Curie when I was a lecturer there (1987-1992). And a professor of statistics and probability there for his entire career, from 1974 to 2013. While we were working on completely different topics, and had divergent political views, we kept an amicable connection throughout the years, as we were living close enough to meet once in a while at the local farmers’ market and have a quick chat. When I was considering my options for pursuing a PhD, while writing a Master thesis on commutative Lie algebras with his father, René Deheuvels, he was one of the people who offered to supervise me (on a topic related with empirical processes, which were his forte). Later, he suggested I wrote a very short introduction to Bayesian statistics in the Que sais-je? collection (where he published three books) and, when my manuscript was found too theoretical, he proposed to publish an expanded version in the Economica collection, which ended up being the French version of The Bayesian Choice. I also remember a very kind email he sent me while I was recovering from my climbing accident, in 2013, as a fellow climber. (For a long while, he would drive to Fontainebleau once or twice a week for bouldering.) As alluded (to) above, Deheuvels’ political views were very conservative, with a proximity to the far-right Club de l’Horloge and a mix of vieille France traditionalism and libertarianism positions. For sure, he never was shy from embarking in controversies, from defending Allègre’s climato-scepticism to backing Séralini’s controversial study on the cancerogenic effects of Mosanto’s transgenic maize.
Archive for The Bayesian Choice
Paul Deheuvels (1948-2026)
Posted in Books, Mountains, University life with tags Bayesian Choice, Bayesian statistics, Book, bouldering, Bourg-la-Reine, climatosceptic, climbing accident, Club de l'Horloge, Economica, empirical process, Fontainebleau, functional estimation, Jussieu, Monsanto, obituary, Paris, Paris 6, Paul Deheuvels, Que sais-je?, The Bayesian Choice, thumb, transgenic corn, UMPC, Université Pierre et Marie Curie on February 5, 2026 by xi'anBayesian Inference: Theory, Methods, Computations [book review]
Posted in Statistics with tags ABC, ABC-MCMC, Bayes factors, Bayesian decision theory, Bayesian inference, Bayesian testing, Bayesian textbook, BIC, book review, capture-recapture, CHANCE, Chapman & Hall, CRC Press, DIC, Jeffreys priors, lizards, statistical inference, subjective versus objective Bayes, The Bayesian Choice, toe clipping, Uppsala University, variational Bayes methods on November 12, 2024 by xi'an
Bayesian Inference: Theory, Methods, Computations by Silvelyn Zwanzig and Rauf Ahmad, both from Uppsala University, is a recent book published by Chapman & Hall / CRC Press. About 300p long (plus appendices), it covers the core aspects of Bayesian inference, namely the decision theoretic motivations, its asymptotic validation, the specifics of estimation and testing, and the computational approximations (MC, MCMC, ABC, VB), with entries on prior specification and Normal linear models. And some R codes. It is (and feels like) constructed from Master and PhD courses (at Uppsala University), with a rigorous mathematical presentation and many examples, some related to biostatistics. Drawings from the first author’s daughter are included in most chapters, to this reviewer’s bemusement. From a further personal viewpoint, the book also reads rather close to my (Bayesian) choice of a Bayesian textbook, which proves rather accurate since several chapters are inspired by my own Bayesian Choice. as acknowledged therein. As well as by the more recent Statistical Decision Theory: Estimation, Testing, and Selection by Liese & Miescke (2008) and Introduction to the Theory of Statistical Inference by Liero & Zwanzig (2011). Witness, for instance, an example of prior construction for capture-recapture experiments on lizards as analysed by my PhD student Dupuis (1995) [with a curious switch to the authors on p.263] and also included in The Bayesian Choice (with drawing 2.9 incorrect in that the lizards there have marks on their backs, instead of the code adopted by the ecologists, namely cutting one specific phalange for each capture).
Other minor quandaries: The usual issue of quoting the wrong edition for creating a method, as when citing Jeffreys (1946) for inventing non-informative priors [p.53], failing to point out the parameterisation invariance of intrinsic losses [p.95]considering that Bayes factors are only relevant for obtaining evidence against the null hypothesis [p.216], recommending BIC and DIC (!) [pp.232-6], advocating sampling importance resampling (SIR) for approximate sampling from the target (omitting infinite variance issues) [p.253], defining annealing as using “several trial distributions” [p.261], a mistake in ABC-MCMC [p.274] since the case when the simulated data is too far from the actual data should lead to a repetition rather than a pure rejection.
All in all, a reasonable textbook with some recent input, but still lacking in originality, if I may subjectively say so.
[Disclaimer about potential self-plagiarism: this post or an edited version of it could possibly appear in my Books Review section in CHANCE.]
a [counter]example of minimaxity
Posted in Books, Kids, Statistics, University life with tags 1984, cross validated, Geometric distribution, George Orwell, least favourable priors, minimaxity, negative binomial distribution, Statistical Decision Theory and Bayesian Analysis, The Bayesian Choice on December 14, 2022 by xi'an
A chance question on X validated made me reconsider about the minimaxity over the weekend. Consider a Geometric G(p) variate X. What is the minimax estimator of p under squared error loss ? I thought it could be obtained via (Beta) conjugate priors, but following Dyubin (1978) the minimax estimator corresponds to a prior with point masses at ¼ and 1, resulting in a constant estimator equal to ¾ everywhere, except when X=0 where it is equal to 1. The actual question used a penalised qaudratic loss, dividing the squared error by p(1-p), which penalizes very strongly errors at p=0,1, and hence suggested an estimator equal to 1 when X=0 and to 0 otherwise. This proves to be the (unique) minimax estimator. With constant risk equal to 1. This reminded me of this fantastic 1984 paper by Georges Casella and Bill Strawderman on the estimation of the normal bounded mean, where the least favourable prior is supported by two atoms if the bound is small enough. Figure 1 in the Negative Binomial extension by Morozov and Syrova (2022) exploits the same principle. (Nothing Orwellian there!) If nothing else, a nice illustration for my Bayesian decision theory course!
In Bayesian statistics, data is considered nonrandom…
Posted in Books, Statistics, University life with tags Bayesian foundations, conditional probability, cross validated, probability theory, randomness, The Bayesian Choice on July 12, 2021 by xi'an
A rather weird question popped up on X validated, namely why does Bayesian analysis rely on a sampling distribution if the data is nonrandom. While a given sample is is indeed a deterministic object and hence nonrandom from this perspective!, I replied that on the opposite Bayesian analysis was setting the observed data as the realisation of a random variable in order to condition upon this realisation to construct a posterior distribution on the parameter. Which is quite different from calling it nonrandom! But, presumably putting too much meaning and spending too much time on this query, I remain somewhat bemused by what line of thought led to this question…
Bayes @ NYT
Posted in Books, Kids, Statistics, University life with tags Alan Turing, applied Bayesian analysis, COVID-19, hierarchical Bayesian modelling, Ireland, journalism, NYT, Oliver Cromwell, The Bayesian Choice, The New York Times, Thomas Bayes, vulgarisation on August 8, 2020 by xi'an
A tribune in the NYT of yesterday on the importance of being Bayesian. When an epidemiologist. Tribune that was forwarded to me by a few friends (and which I missed on my addictive monitoring of the journal!). It is written by , a Canadian journalist writing about mathematics (and obviously statistics). And it brings to the general public the main motivation for adopting a Bayesian approach, namely its coherent handling of uncertainty and its ability to update in the face of new information. (Although it might be noted that other flavours of statistical analysis are also able to update their conclusions when given more data.) The COVID situation is a perfect case study in Bayesianism, in that there are so many levels of uncertainty and imprecision, from the models themselves, to the data, to the outcome of the tests, &tc. The article is journalisty, of course, but it quotes from a range of statisticians and epidemiologists, including Susan Holmes, whom I learned was quarantined 105 days in rural Portugal!, developing a hierarchical Bayes modelling of the prevalent SEIR model, and David Spiegelhalter, discussing Cromwell’s Law (or better, humility law, for avoiding the reference to a fanatic and tyrannic Puritan who put Ireland to fire and the sword!, and had in fact very little humility for himself). Reading the comments is both hilarious (it does not take long to reach the point when Trump is mentioned, and Taleb’s stance on models and tails makes an appearance) and revealing, as many readers do not understand the meaning of Bayes’ inversion between causes and effects, or even the meaning of Jeffreys’ bar, |, as conditioning.
