**W**hen [X’ed] seeking a simple proof of the Pitman-Koopman-Darmois lemma [that exponential families are the only types of distributions with constant support allowing for a fixed dimension sufficient statistic], I came across a 1962 Stanford technical report by Don Fraser containing a short proof of the result. Proof that I do not fully understand as it relies on the notion that the likelihood function itself is a minimal sufficient statistic.

## Archive for Don Fraser

## Darmois, Koopman, and Pitman

Posted in Books, Statistics with tags cross validated, Don Fraser, exponential families, George Darmois, mathematical statistics, Pitman-Koopman theorem, proof, Stanford University, sufficient statistics on November 15, 2017 by xi'an## Bayes is typically wrong…

Posted in pictures, Running, Statistics, Travel, University life with tags Bayesian Fiducial & Frequentist Conference, Bayesian foundations, Boston, Boston harbour, Don Fraser, fiducial inference, Harvard University, matching priors, Nancy Reid, profile likelihood, skyline, sunrise on May 3, 2017 by xi'an**I**n Harvard, this morning, Don Fraser gave a talk at the Bayesian, Fiducial, and Frequentist conference where he repeated *[as shown by the above quote]* the rather harsh criticisms on Bayesian inference he published last year in Statistical Science. And which I discussed a few days ago. The “wrongness” of Bayes starts with the completely arbitrary choice of the prior, which Don sees as unacceptable, and then increases because the credible regions are not confident regions, outside natural parameters from exponential families (Welch and Peers, 1963). And one-dimensional parameters using the profile likelihood (although I cannot find a proper definition of what the profile likelihood is in the paper, apparently a plug-in version that is not a genuine likelihood, hence somewhat falling under the same *this-is-not-a-true-probability* cleaver as the disputed Bayesian approach).

“I expect we’re all missing something, but I do not know what it is.”D.R. Cox, Statistical Science, 1994

And then Nancy Reid delivered a plenary lecture *“Are we converging?”* on the afternoon that compared most principles (including objective if not subjective Bayes) against different criteria, like consistency, nuisance elimination, calibration, meaning of probability, and so on. In an highly analytic if pessimistic panorama. (The talk should be available on line at some point soon.)

## Bayes posterior just quick and dirty on X’idated

Posted in Statistics, Travel, University life with tags Bayesian inference, confidence region, cross validated, Don Fraser, foundations on February 22, 2012 by xi'an**A**s a coincidence, I noticed that Don Fraser’s recent discussion paper *`Is Bayes posterior just quick and dirty confidence?’* will be discussed this Friday (18:00 UTC) on the Cross Validated Journal Club. I do not know whether or not to interpret the information “The author confirmed his presence at the event” as meaning Don Fraser will be on line to discuss his paper with X’ed members Feel free to join anyway if you have 20 reputation points or plan to get those by Friday! (I will be in the train coming back from Oxford. Oxford, England, not Mississippi!)

## Improving convergence of Data Augmentation [published]

Posted in Statistics with tags Data augmentation, Don Fraser, Fort Collins, Richard Tweedie, Statistical Science on November 4, 2011 by xi'an**O**ur paper with Jim Hobert and Vivek Roy, Improving the Convergence Properties of the Data Augmentation Algorithm with an Application to Bayesian Mixture Modeling, has now appeared in *Statistical Science* and is available on **Project Euclid**. (For IMS members, at least.) Personally, this is an important paper, not only for providing an exact convergence evaluation for mixtures, not only for sharing exciting research days with my friends Jim and Vivek, but also for finalising a line of research somehow started in 1993 when Richard Tweedie visited me in Paris and when I visited him in Fort Collins… Coincidentally, my discussion of Don Fraser’s provocative Is Bayes Posterior just Quick and Dirty Confidence? also appeared in this issue of *Statistical Science*.

## Don Fraser’s rejoinder

Posted in Books, Statistics, University life with tags Bayesian inference, Biometrika, confidence region, Don Fraser, Error and Inference, frequentist inference, Statistical Science on August 24, 2011 by xi'an

“How can a discipline, central to science and to critical thinking, have two methodologies, two logics, two approaches that frequently give substantially different answers to the same problems. Any astute person from outside would say “Why don’t they put their house in order?””Don Fraser

**F**ollowing the discussions of his *Statistical Science* paper ** Is Bayes posterior just quick and dirty confidence?**, by Kesar Singh and Minge Xie, Larry Wasserman (who coined the neologism

*Frasian*for the occasion), Tong Zhang, and myself,

**Don Fraser has written his rejoinder to the discussion (although in**

*Biometrika*style it is for

*Statistical Science*!). His conclusion that “

*no one argued that the use of the conditional probability lemma with an imaginary input had powers beyond confidence, supernatural powers*” is difficult to escape, as I would not dream of promoting a super-Bayes jumping to the rescue of bystanders misled by evil frequentists!!! More seriously, this rejoinder makes me reflect on lectures from the past years, from those on the diverse notions of probability (Jeffreys, Keynes, von Mises, and Burdzy) to those on scientific discovery (mostly Seber‘s, and the promising

**by Mayo and Spanos I just received).**

*Error and Inference*