Mike Titterington [in memoriam²]

irreverent Mike [in memoriam]

While I could not find an on-line picture of Mike Titterington, another testimony to his modesty and selflessness, I remembered this series of sketches on priors he made for the Bulletin in Applied Statistics in 1982, under the title Irreverent Bayes!

Mike Titterington (1945-2023)

Most sadly, I just heard from Glasgow that my friend and coauthor Mike Titterington passed away last weekend. While a significant figure in the field and a precursor in many ways, from mixtures to machine learning, Mike was one of the kindest persons ever, tolerant to a fault and generous with his time, and I enjoyed very much my yearly visits to Glasgow to work with him (and elope to the hills). This was also the time he was the (sole) editor of Biometrika and to this day I remain amazed at the amount of effort he dedicated to it, annotating every single accepted paper with his red pen during his morning bus commute and having the edited copy mailed to the author(s). The last time I saw him was in October 2019, when I was visiting the University of Edinburgh and the newly created Bayes Centre, and he came to meet me for an afternoon tea, despite being in poor health… Thank you for all these years, Mike!

Finite mixture models do not reliably learn the number of components

When preparing my talk for Padova, I found that Diana Cai, Trevor Campbell, and Tamara Broderick wrote this ICML / PLMR paper last year on the impossible estimation of the number of components in a mixture.

“A natural check on a Bayesian mixture analysis is to establish that the Bayesian posterior on the number of components increasingly concentrates near the truth as the number of data points becomes arbitrarily large.” Cai, Campbell & Broderick (2021)

Which seems to contradict [my formerly-Glaswegian friend] Agostino Nobile  who showed in his thesis that the posterior on the number of components does concentrate at the true number of components, provided the prior contains that number in its support. As well as numerous papers on the consistency of the Bayes factor, including the one against an infinite mixture alternative, as we discussed in our recent paper with Adrien and Judith. And reminded me of the rebuke I got in 2001 from the late David McKay when mentioning that I did not believe in estimating the number of components, both because of the impact of the prior modelling and of the tendency of the data to push for more clusters as the sample size increased. (This was a most lively workshop Mike Titterington and I organised at ICMS in Edinburgh, where Radford Neal also delivered an impromptu talk to argue against using the Galaxy dataset as a benchmark!)

“In principle, the Bayes factor for the MFM versus the DPM could be used as an empirical criterion for choosing between the two models, and in fact, it is quite easy to compute an approximation to the Bayes factor using importance sampling” Miller & Harrison (2018)

This is however a point made in Miller & Harrison (2018) that the estimation of k logically goes south if the data is not from the assumed mixture model. In this paper, Cai et al. demonstrate that the posterior diverges, even when it depends on the sample size. Or even the sample as in empirical Bayes solutions.

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.