An ISBA World meeting is always an exciting event that verges on the sensory overload! The more when one’s flight is perversely designed to land at my usual bedtime. (I tried waking up very early and running for an hour before catching the plane but this did not make me doze for more than one hour or two in the plane.) To explain why I missed the first two foundation lectures of the day, including the one by my dear friend Sylvia Richardson, as I was still resting (to avoid repeating my fainting upon arrival as happened last year, or later as). Incidentally, these lectures made me realise I had given one in Kyoto (on ABC) in 2012. I however managed to attend David Dunson’s wide recap on Bayesian clustering(s), with slides ChatGPT confused with posters, hence a massive information content had I been able to read them from my seat! More fundamentally, the residual difficulty being the very notion of cluster itself. And a jump back in time with Fumiyasu Komaki going over his corpus of works on the decision theoretic properties of Bayesian predictives when the Kullback-Leibler divergence is the loss function. An interesting feature of his findings is that comparing priors in that sense is equivalent to comparing them for point estimation in Normal and Poisson cases, but not in the Gamma case, for no reason I can fathom. A philosophical point of contention of mine’s was the introduction of two Jeffreys priors when observed data and predicted data are from different distributions (calibrated by the same parameter θ) since it calls for a Lindley’s style criticism that a realisation not (yet) observed modifies the prior distribution on θ. If possibly leading to improved estimation.
Archive for admissibility
ISBA 2026¹
Posted in Kids, pictures, Statistics, Travel, University life with tags admissibility, Bayesian predictive, clustering, conference, deadline, foundation lectures, ISBA, ISBA 2026, Japan, Jeffreys-Lindley paradox, Kyoto, Kyushu, logo, mixtures of distributions, Nagoya, registration fees, Shachihoko, Stein effect, student membership, Tokyo, WINC AICHI on June 30, 2026 by xi'ane-values in Chennai
Posted in Books, pictures, Running, Statistics, Travel, University life with tags Abraham Wald, admissibility, Bayes factors, Bayesian hypothesis testing, Benjamini, BIRSCMI, Chennai, Chennai Mathematical Institute, complete class theorems, confidence sequence, Dickey-Savage ratio, e-values, empirical Bayes methods, FDRs, Hochberg, Neyman-Pearson tests, p-values, sequential testing, south Indian cuisine, Tamil Nadu on July 23, 2025 by xi'an
To recap, I thus attended the BIRS-CMI workshop 25w5482 at the Chennai Mathematical Institute, Navalur, Tamil Nadu, in early July, for being intrigued by the developments around the concept. And enjoyed the week, from partaking in the company of friendly and enthusiastic academics to the exposure of new views and concepts, mostly remote from mine’s. Recall that an e-value attached to an hypothesis H described as a collection of distributions is a non-negative random variable E with expectation less than 1 for E~Q and all Q ∈ H. When a stopping rule is involved, the e-value is extended into an e-process. (Beyond Aaditya Ramdas’ E-book, Ruodu Wang also wrote a “tiny” review.) Aaditya Ramdas recalled in his introduction of the workshop that e-values are fundamentally equivalent to p-values and confidence intervals. And that a confidence sequence is a sequence of confidence intervals that contains the true value for all time steps t’s with a probability of at least 1-α.
The talks reflected a general belief in α levels and in Neyman-Pearsonian likelihood ratio optimality in simple vs simple settings, considering extension for sequential analysis settings, anytime inference, universality under general alternatives, and connections with FDRs, incl. Benjamini & Hochberg solution, but pointed out a lack of middle ground between frequentists and Bayesians.
“e-values have a clear interpretation in terms of betting and are closely related to likelihood ratios and other Bayes factor. At the same time, e–values do not require prior distributions conditional on the null and alternative hypotheses”
Although David R. Bickel attempted a Bayesian version, using a marginal likelihood ratio within betting settings, that is an incoming American Statistician paper. I may have being missing some aspects due to a lack of sleep the night before (!), but I find the attempt resulting in a fairly unusual vision of Bayesian testing as either not depending on any parameter or on the opposite using a family of priors. I did not understand either the “criticism” that the predictive depends on the prior and felt that this representation was bending in a rather onsiderable way the Bayesian perspective towards achieving a certain degree of agreement with p– and e-value notions, to conclude that the Bayes factor is an e-value. (As an aside, this may be the first paper that cited our critical review of Aitkin! Similarly, Shubhada Agrawal mentioned Roger Farrell in his talk, with whom we wrote a complete class Annals paper in the late 1980’s.) Nikos Ignatiadis also explored Empirical Bayes e-values, while Ben Chugg gave a presentation (constrained) admissibility, albeit under type-I error constraints that makes Bayes infeasible and using Neyman-Pearsonian loss functions. On the last day, Peter Grünwald tried for some BFF cohesion with openings on e-posteriors, treating hypothesis testing losses symmetrically, defining it as an inverse of e-values but incorporating pseudo-posteriors of many flavours like confidence, inferential, and fiducial distributions. He also mentioned a Savage-Dickey version while using an arbitrary prior, which is also an e-value, but with upper & lower meanings, again with measure issues
Given the hosting of the workshop in the Chennai Mathematical Institute, which is quite far from the centre of town (much closer to Mahabalipuram!), I did not visit Chennai but enjoyed the South Indian cuisine (albeit missing some fierceness in the spices!) and local fruits from street stands, if being sorry I could not find cocoa pods from nearby Kerala.
William (Bill) Strawderman (1941-2024)
Posted in pictures, Statistics, University life with tags admissibility, apple brandy, Bayesian decision theory, Bill Strawderman, Calvados, Charles Dickens, credible intervals, Institut de Mathématiques de Jussieu, James-Stein estimator, minimaxity, New Brunswick, New Jersey, Paris 6, Pitman nearness, Rutgers University, shrinkage estimation, Université de Rouen on October 3, 2024 by xi'an
Earlier today, I was informed by several of our mutual friends that my long-time friend Bill Strawderman had sadly passed away yesterday, after fighting a cancer for the past months. I remember quite clearly meeting Bill in the Fall of 1988 in front of White Hall, which hosted the Cornell maths department at the time, as he was visiting George Casella from Rutgers where he spent most of his career. I was most eager to meet him as I had worked on several of his landmark papers during my PhD on shrinkage estimation, as well as a bit impressed. But his kindness, modesty, and congenial personality quickly put me at ease and we spent the rest of his visit discussing shrinkage but also literature and music. Especially Dickens! After that we met and collaborated quite regularly, to the point he started visiting France upon my return, at Paris 6 (Pierre & Marie Curie) University first, and then in Rouen, where he became a adjunct professor and launched a life-long collaboration and friendship with Dominique Fourdrinier. As my interest in shrinkage estimation dwindled along the years, we did not keep collaborating for the past two decades, but we remained in touch and I was very happy to participate in his 80th anniversary celebration in Rutgers two years ago. His contributions to the field are notable and several papers of his were part of the Bayesian classics I was giving my graduate class a few years ago. From the fabulous minimaxity paper of 1984, along with George Casella, to admissible estimators dominating the positive-part James-Stein estimator, to sufficient conditions of minimaxity for proper Bayes estimators, to decision theoretic properties of Bayesian credible interval estimators, to loss estimation, not to mention his more applied side… Besides his fabulous sense of humour, which made many evenings with him memorable, I will also cherish the memory of a bon vivant who liked good food and good wines, incl. the Calvados apple brandy I would bring him at each of my visits.
principles of uncertainty (second edition)
Posted in Books, Statistics, Travel, University life with tags admissibility, École Polytechnique, book review, Bruno de Finetti, Carnegie Mellon University, causation, Chapman & Hall, CMU, CRC Press, Fourier transform, Jacques Neveu, Jay Kadane, John Maynard Keynes, measure theory, meta-analysis, minimaxity, Pitman-Koopman theorem, principles of uncertainty, second edition, Stein's paradox, utility theory, version on July 21, 2020 by xi'an
A new edition of Principles of Uncertainty is about to appear. I was asked by CRC Press to review the new book and here are some (raw) extracts from my review. (Some comments may not apply to the final and published version, mind.)
In Chapter 6, the proof of the Central Limit Theorem utilises 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 its probability notes in Polytechnique. Which went under the more formal denomination of convolution, with the same (commendable) purpose of avoiding Fourier transforms. If anything, I would have favoured a slightly more condensed presentation in less than 8 pages. Is Corollary 6.5.8 useful or even correct??? I do not think so because the non-centred average rescaled by √n diverges almost surely. For the same reason, I object to the very first sentence of Section 6.5 (p.246)
In Chapter 7, I found a nice mention of (Hermann) Rubin’s insistence on not separating probability and utility as only the product matters. And another fascinating quote from Keynes, not from his early statistician’s years, but in 1937 as an established economist
“The sense in which I am using the term uncertain is that in which the prospect of a European war is uncertain, or the price of copper and the rate of interest twenty years hence, or the obsolescence of a new invention, or the position of private wealth-owners in the social system in 1970. About these matters there is no scientific basis on which to form any calculable probability whatever. We simply do not know. Nevertheless, the necessity for action and for decision compels us as practical men to do our best to overlook this awkward fact and to behave exactly as we should if we had behind us a good Benthamite calculation of a series of prospective advantages and disadvantages, each multiplied by its appropriate probability, waiting to the summed.”
(is the last sentence correct? I would have expected, pardon my French!, “to be summed”). Further interesting trivia on the criticisms of utility theory, including de Finetti’s role and his own lack of connection with subjective probability principles.
In Chapter 8, a major remark (iii) is found p.293 about the fact that a conjugate family requires a dominating measure (although this is expressed differently since the book shies away from introducing measure theory, ) reminds me of a conversation I had with Jay when I visited Carnegie Mellon in 2013 (?). Which exposes the futility of seeing conjugate priors as default priors. It is somewhat surprising that a notion like admissibility appears as a side quantity when discussing Stein’s paradox in 8.2.1 [and then later in Section 9.1.3] while it seems to me to be central to Bayesian decision theory, much more than the epiphenomenon that Stein’s paradox represents in the big picture. But the book dismisses minimaxity even faster in Section 9.1.4:
As many who suffer from paranoia have discovered, one can always dream-up an even worse possibility to guard against. Thus, the minimax framework is unstable. (p.336)
Interesting introduction of the Wishart distribution to kindly handle random matrices and matrix Jacobians, with the original space being the p(p+1)/2 real space (implicitly endowed with the Lebesgue measure). Rather than a more structured matricial space. A font error makes Corollary 8.7.2 abort abruptly. The space of positive definite matrices is mentioned in Section8.7.5 but still (implicitly) corresponds to the common p(p+1)/2 real Euclidean space. Another typo in Theorem 8.9.2 with a Frenchised version of Dirichlet, Dirichelet. Followed by a Dirchlet at the end of the proof (p.322). Again and again on p.324 and on following pages. I would object to the singular in the title of Section 8.10 as there are exponential families rather than a single one. With no mention made of Pitman-Koopman lemma and its consequences, namely that the existence of conjugacy remains an epiphenomenon. Hence making the amount of pages dedicated to gamma, Dirichlet and Wishart distributions somewhat excessive.
In Chapter 9, I noticed (p.334) a Scheffe that should be Scheffé (and again at least on p.444). (I love it that Jay also uses my favorite admissible (non-)estimator, namely the constant value estimator with value 3.) I wonder at the worth of a ten line section like 9.3, when there are delicate issues in handling meta-analysis, even in a Bayesian mood (or mode). In the model uncertainty section, Jay discuss the (im)pertinence of both selecting one of the models and setting independent priors on their respective parameters, with which I disagree on both levels. Although this is followed by a more reasonable (!) perspective on utility. Nice to see a section on causation, although I would have welcomed an insert on the recent and somewhat outrageous stand of Pearl (and MacKenzie) on statisticians missing the point on causation and counterfactuals by miles. Nonparametric Bayes is a new section, inspired from Ghahramani (2005). But while it mentions Gaussian and Dirichlet [invariably misspelled!] processes, I fear it comes short from enticing the reader to truly grasp the meaning of a prior on functions. Besides mentioning it exists, I am unsure of the utility of this section. This is one of the rare instances where measure theory is discussed, only to state this is beyond the scope of the book (p.349).
prior against truth!
Posted in Books, Kids, Statistics with tags admissibility, Bayesian estimation, Bill Strawderman, consistency, cross validated, George Casella, minimaxity, support on June 4, 2018 by xi'an
A question from X validated had interesting ramifications, about what happens when the prior does not cover the true value of the parameter (assuming there ? In fact, not so much in that, from a decision theoretic perspective, the fact that that π(θ⁰)=0, or even that π(θ)=0 in a neighbourhood of θ⁰ does not matter [too much]. Indeed, the formal derivation of a Bayes estimator as minimising the posterior loss means that the resulting estimator may take values that were “impossible” from a prior perspective! Indeed, taking for example the posterior mean, the convex combination of all possible values of θ under π may well escape the support of π when this support is not convex. Of course, one could argue that estimators should further be restricted to be possible values of θ under π but that would reduce their decision theoretic efficiency.
An example is the brilliant minimaxity result by George Casella and Bill Strawderman from 1981: when estimating a Normal mean μ based on a single observation xwith the additional constraint that |μ|<ρ, and when ρ is small enough, ρ≤1.0567 quite specifically, the minimax estimator for this problem under squared error loss corresponds to a (least favourable) uniform prior on the pair {−ρ,ρ}, meaning that π gives equal weight to −ρ and ρ (and none to any other value of the mean μ). When ρ increases above this bound, the least favourable prior sees its support growing one point at a time, but remaining a finite set of possible values. However the posterior expectation, 𝔼[μ|x], can take any value on (−ρ,ρ).
In an even broader suspension of belief (in the prior), it may be that the prior has such a restricted support that it cannot consistently estimate the (true value of the) parameter, but the associated estimator may remain admissible or minimax.
