David Cox (1924-2022)

It is with much sadness that I heard from Oxford yesterday night that David Cox had passed away. Hither goes a giant of the field, whose contributions to theoretical and methodological statistics are enormous and whose impact on society is truly exceptional. He was the first recipient of the International Prize in Statistics in 2016 (aka the “Nobel of Statistics”) among many awards and a Fellow of the Royal Society among many other recognitions. He was also the editor of Biometrika for 25 years (!) and was still submitting papers to the journal a few month ago. Statistical Science published a conversation between Nancy Reid and him that tells a lot about the man and his amazing modesty. While I had met him in 1989, when he was visiting Cornell University as a distinguished visitor (and when I drove him to the house of Anne and George Casella for dinner once), then again in the 1990s when he came on a two-day visit to CREST,  we only really had a significant conversation in 2011 (!), when David and I attended the colloquium in honour of Mike Titterington in Glasgow and he proved to be most interested in the ABC algorithm. He published a connected paper in Biometrika the year after, with Christiana Katsonaki. We met a few more times later, always in Oxford, to again discuss ABC. In each occasion, he was incredibly kind and considerate.

ordered allocation sampler

Recently, Pierpaolo De Blasi and María Gil-Leyva arXived a proposal for a novel Gibbs sampler for mixture models. In both finite and infinite mixture models. In connection with Pitman (1996) theory of species sampling and with interesting features in terms of removing the vexing label switching features.

“The key idea is to work with the mixture components in the random order of appearance in an exchangeable sequence from the mixing distribution (…) In accordance with the order of appearance, we derive a new Gibbs sampling algorithm that we name the ordered allocation sampler. “

This central idea is thus a reinterpretation of the mixture model as the marginal of the component model when its parameter is distributed as a species sampling variate. An ensuing marginal algorithm is to integrate out the weights and the allocation variables to only consider the non-empty component parameters and the partition function, which are label invariant. Which reminded me of the proposal we made in our 2000 JASA paper with Gilles Celeux and Merrilee Hurn (one of my favourite papers!). And of the [first paper in Statistical Methodology] 2004 partitioned importance sampling version with George Casella and Marty Wells. As in the later, the solution seems to require the prior on the component parameters to be conjugate (as I do not see a way to produce an unbiased estimator of the partition allocation probabilities).

The ordered allocation sample considers the posterior distribution of the different object made of the parameters and of the sequence of allocations to the components for the sample written in a given order, ie y¹,y², &tc. Hence y¹ always gets associated with component 1, y² with either component 1 or component 2, and so on. For this distribution, the full conditionals are available, incl. the full posterior on the number m of components, only depending on the data through the partition sizes and the number m⁺ of non-empty components. (Which relates to the debate as to whether or not m is estimable…) This sequential allocation reminded me as well of an earlier 2007 JRSS paper by Nicolas Chopin. Albeit using particles rather than Gibbs and applied to a hidden Markov model. Funny enough, their synthetic dataset univ4 almost resembles the Galaxy dataset (as in the above picture of mine)!

postdoctoral position in computational statistical physics and machine learning

Relevant statistics for Bayesian model choice [hot off the press!]

Our paper about evaluating statistics used for ABC model choice has just appeared in Series B! It somewhat paradoxical that it comes out just a few days after we submitted our paper on using random forests for Bayesian model choice, thus bypassing the need for selecting those summary statistics by incorporating all statistics available and letting the trees automatically rank those statistics in term of their discriminating power. Nonetheless, this paper remains an exciting piece of work (!) as it addresses the more general and pressing question of the validity of running a Bayesian analysis with only part of the information contained in the data. Quite usefull in my (biased) opinion when considering the emergence of approximate inference already discussed on this ‘Og…

[As a trivial aside, I had first used fresh from the press(es) as the bracketted comment, before I realised the meaning was not necessarily the same in English and in French.]