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 Stein effect
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'anStein estimation [not a book review]
Posted in Books, pictures, Statistics, Travel, University life with tags book review, James-Stein estimator, location-scale parameterisation, normal mean, Rutgers University, springer, Stein effect, William Strawderman on October 16, 2024 by xi'an
d≥3 strikes again
Posted in Statistics, University life with tags Boltzmann-Grad limit, Brownian motion, CLT, coupling, Markov process, null recurrence, seminar, Stein effect, transience, University of Bristol, Wiener process on April 23, 2024 by xi'an
Yesterday, Bálint Tóth (University of Bristol and Alfréd Rényi Institute of Mathematics) came to Paris Dauphine for a seminar on the Botlzmann-Grad limit and the existence of a central (double) limit theory. Which was somewhat related with the above video of an earlier seminar, albeit without the first part on the historical roots of the problem. This was a brilliant talk as quite accessible to the entirety of the lab, while providing detailed entries on the mechanism leading to the CLT, in particular the substitution of the physical process by a Markovian(ised) process that stayed closed enough to the original for long enough, a sort of (anti-)coupling idea I had never met before. The other (personally) striking feature of the seminar was the occurrence of the boundary d=3 on the dimension of the process, The same boundary as in the Stein phenomenon (and the difference from recurrent to transient in random walks). But I could not see a clear connection with the present challenge.
an improvable Rao–Blackwell improvement, inefficient maximum likelihood estimator, and unbiased generalized Bayes estimator
Posted in Books, Statistics, University life with tags best unbiased estimator, complete statistics, maximum likelihood estimation, Pitman best equivariant estimator, R-bloggers, Rao-Blackwell theorem, Stein effect, The American Statistician, uniform distribution on February 2, 2018 by xi'an
In my quest (!) for examples of location problems with no UMVU estimator, I came across a neat paper by Tal Galili [of R Bloggers fame!] and Isaac Meilijson presenting somewhat paradoxical properties of classical estimators in the case of a Uniform U((1-k)θ,(1+k)θ) distribution when 0<k<1 is known. For this model, the minimal sufficient statistic is the pair made of the smallest and of the largest observations, L and U. Since this pair is not complete, the Rao-Blackwell theorem does not produce a single and hence optimal estimator. The best linear unbiased combination [in terms of its variance] of L and U is derived in this paper, although this does not produce the uniformly minimum variance unbiased estimator, which does not exist in this case. (And I do not understand the remark that
“Any unbiased estimator that is a function of the minimal sufficient statistic is its own Rao–Blackwell improvement.”
as this hints at an infinite sequence of improvement.) While the MLE is inefficient in this setting, the Pitman [best equivariant] estimator is both Bayes [against the scale Haar measure] and unbiased. While experimentally dominating the above linear combination. The authors also argue that, since “generalized Bayes rules need not be admissible”, there is no guarantee that the Pitman estimator is admissible (under squared error loss). But given that this is a uni-dimensional scale estimation problem I doubt very much there is a Stein effect occurring in this case.
Charles M. Stein [1920-2016]
Posted in Books, pictures, Statistics, University life with tags admissibility, Charles Stein, Iraq War, James-Stein estimator, shrinkage estimation, Stanford University, Stein effect, Stein method, University of California Berkeley, Vietnam War on November 26, 2016 by xi'an
I have just heard that Charles Stein, Professor at Stanford University, passed away last night. Although the following image is definitely over-used, I truly feel this is the departure of a giant of statistics. He has been deeply influential on the fields of probability and mathematical statistics, primarily in decision theory and approximation techniques. On the first field, he led to considerable changes in the perception of optimality by exhibiting the Stein phenomenon, where the aggregation of several admissible estimators of unrelated quantities may (and will) become inadmissible for the joint estimation of those quantities! Although the result can be explained by mathematical and statistical reasoning, it was still dubbed a paradox due to its counter-intuitive nature. More foundationally, it led to expose the ill-posed nature of frequentist optimality criteria and certainly contributed to the Bayesian renewal of the 1980’s, before the MCMC revolution. (It definitely contributed to my own move, as I started working on the Stein phenomenon during my thesis, before realising the fundamentally Bayesian nature of the domination results.)
“…the Bayesian point of view is often accompanied by an insistence that people ought to agree to a certain doctrine even without really knowing what this doctrine is.” (Statistical Science, 1986)
The second major contribution of Charles Stein was the introduction of a new technique for normal approximation that is now called the Stein method. It relies on a differential operator and produces estimates of approximation error in Central Limit theorems, even in dependent settings. While I am much less familiar with this aspect of Charles Stein’s work, I believe the impact it has had on the field is much more profound and durable than the Stein effect in Normal mean estimation.
(During the Vietnam War, he was quite active in the anti-war movement and the above picture from 2003 shows that his opinions had not shifted over time!) A giant truly has gone.
