Archive for Bayesian tests of hypotheses

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World statistics day

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , on October 20, 2015 by xi'an

Today is October 20, World Statistics Day as launched by the UN. And supported by local and international societies. In connection with that day, among many events, the RSS will be hosting a reception, China will hold a seminar in… Xi’an, how appropriate!, my friend Kerrie Mengersen will give a talk at the Queensland University of Technology (QUT) on The power and promise of immersive virtual environments. (Bringing her pet crocodile to the talk, hopefully!)

Leuven9And I will also give a talk in Louvain-la-Neuve, Belgium, on Le délicat dilemme des tests d’hypothèse et de leur résolution bayésienne. At ISBA, which stands for Institute of Statistics, Biostatistics and Actuarial Sciences and not for the Bayesian society!. within UCL, which stands for Université Catholique de Louvain and not for University College London! (And which is not to be confused with the Katholieke Universiteit Leuven, in Leuven, where I was last year for MCqMC. About 25 kilometers away.) In case this is not confusing enough, here are my slides (in English, while the talk will be in French):

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métro static

Posted in Kids, Statistics, Travel with tags , , , , , , on July 19, 2015 by xi'an

[In the train shuttle at Birmingham airport, two young guys, maybe back from SPA 2015, discussing signal processing:]

– In Bayesian statistics, they use a different approach to testing hypotheses… You see, they put priors on the different hypotheses…

– But in the end it all boils down to concentration inequalities…

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O’Bayes15: my tutorial

Posted in Books, Kids, pictures, Running with tags , , , , , on June 1, 2015 by xi'an

Valencia, Feb. 21Here are the slides I made for a short tutorial I will deliver this afternoon for the opening day of the International Workshop on Objective Bayes Methodology, O-Bayes15, held in the city of Valencià, so intricately linked with Bayesians and Bayesianism. The more so as we celebrating this time the career and life of our dear friend Susie. Celebrating with talks and stories, morning runs and afternoon drinks, laughs, tears, and more laughs, even though they cannot equate Susie’s unique and vibrant communicative laugh. I will remember how, at O’Bayes 13, Susie was the one who delivered this tutorial. And how, despite physical frailty and fatigue, she did with her usual energy and mental strength. And obviously again with laugh. I will also remember that the last time I visited Valencià, it was for Anabel Forte’s thesis defence, upon invitation from Susie, and that we had a terrific time, from discussing objective Bayes ideas to eating and drinking local goodies, to walking around the grandiose monuments just built (which presumably contributed to ruin the City of Valencià for quite a while!)

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the maths of Jeffreys-Lindley paradox

Posted in Books, Kids, Statistics with tags , , , , , , , on March 26, 2015 by xi'an

75b18-imagedusparadrapCristiano Villa and Stephen Walker arXived on last Friday a paper entitled On the mathematics of the Jeffreys-Lindley paradox. Following the philosophical papers of last year, by Ari Spanos, Jan Sprenger, Guillaume Rochefort-Maranda, and myself, this provides a more statistical view on the paradox. Or “paradox”… Even though I strongly disagree with the conclusion, namely that a finite (prior) variance σ² should be used in the Gaussian prior. And fall back on classical Type I and Type II errors. So, in that sense, the authors avoid the Jeffreys-Lindley paradox altogether!

The argument against considering a limiting value for the posterior probability is that it converges to 0, 21, or an intermediate value. In the first two cases it is useless. In the medium case. achieved when the prior probability of the null and alternative hypotheses depend on variance σ². While I do not want to argue in favour of my 1993 solution

\rho(\sigma) = 1\big/ 1+\sqrt{2\pi}\sigma

since it is ill-defined in measure theoretic terms, I do not buy the coherence argument that, since this prior probability converges to zero when σ² goes to infinity, the posterior probability should also go to zero. In the limit, probabilistic reasoning fails since the prior under the alternative is a measure not a probability distribution… We should thus abstain from over-interpreting improper priors. (A sin sometimes committed by Jeffreys himself in his book!)

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my life as a mixture [BAYSM 2014, Wien]

Posted in Books, Kids, Mountains, pictures, Statistics, Travel, University life with tags , , , , , , , , , , on September 12, 2014 by xi'an

Next week I am giving a talk at BAYSM in Vienna. BAYSM is the Bayesian Young Statisticians meeting so one may wonder why, but with Chris Holmes and Mike West, we got invited as more… erm… senior speakers! So I decided to give a definitely senior talk on a thread pursued throughout my career so far, namely mixtures. Plus it also relates to works of the other senior speakers. Here is the abstract for the talk:

Mixtures of distributions are fascinating objects for statisticians in that they both constitute a straightforward extension of standard distributions and offer a complex benchmark for evaluating statistical procedures, with a likelihood both computable in a linear time and enjoying an exponential number of local models (and sometimes infinite modes). This fruitful playground appeals in particular to Bayesians as it constitutes an easily understood challenge to the use of improper priors and of objective Bayes solutions. This talk will review some ancient and some more recent works of mine on mixtures of distributions, from the 1990 Gibbs sampler to the 2000 label switching and to later studies of Bayes factor approximations, nested sampling performances, improper priors, improved importance samplers, ABC, and a inverse perspective on the Bayesian approach to testing of hypotheses.

I am very grateful to the scientific committee for this invitation, as it will give me the opportunity to meet the new generation, learn from them and in addition discover Vienna where I have never been, despite several visits to Austria. Including its top, the Großglockner. I will also give a seminar in Linz the day before. In the Institut für Angewandte Statistik.

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