Francis Comets (1956-2022)

Francis Comets, with whom I taught at Polytechnique in the early 2000’s, and whom I highly respected, has most sadly died on June 6. Here is a eulogy written by Patrick Cattiaux, Giambattista Giacomin, and Lorenzo Zambotti, on the site of the Société Mathématique de France (translated from the French).

Francis was a rare person. Combining both a form of conformism and a surprising originality, he marked all those who knew him: colleagues, relatives, friends. A former student of the École Normale Supérieure de Saint Cloud, in 1987 he defended a Thèse d’État at the University of Paris Sud on problems of large deviations in connection with models of statistical physics. Very quickly he demonstrated his appetite for various fields combining probability, statistics and physics. Just check out his list of publications. Francis will remain as one of the pioneers in France in the study of models in random environments for which his contributions are internationally recognized, symbolized by the Ito prize from the Bernoulli Society received in 2015. Beyond a leading scientific activity, Francis has been for forty years a major player in the structuring of mathematics in France. First assistant at the University of Paris X, then Professor at Marne la Vallée and finally at Paris 7 (which over time became Paris Diderot and now Université Paris Cité), he has, during his academic career, spared no effort in serving the community. Director of the Laboratory of Probability and Random Models, co-founder of the Fondation Sciences Mathématiques de Paris, part-time professor at the École Polytechnique, he has devoted a very large part of his time to the French mathematical community. His students and his colleagues have found in Francis listening, empathy, competence and that hint of surprise that leads to curiosity. His friends and loved ones will express the deep and personal feelings that bound them to a rare being, as mentioned above. The French mathematical community joins in the grief of his family and friends at such a painful time.

extinction minus one

The riddle from The Riddler of 19 Feb. is about the Bernoulli Galton-Watson process, where each individual in the population has one or zero descendant with equal probabilities: Starting with a large population os size N, what is the probability that the size of the population on the brink of extinction is equal to one? While it is easy to show that the probability the n-th generation is extinct is

I could not find a way to express the probability to hit one and resorted to brute force simulation, easily coded

for(t in 1:(T<-1e8)){N=Z=1e4 
while(Z>1)Z=rbinom(1,Z,.5)
F=F+Z}
F/T

which produces an approximate probability of 0.7213 or 0.714. The impact of N is quickly vanishing, as expected when the probability to reach 1 in one generation is negligible…

However, when returning to Dauphine after a two-week absence, I presented the problem with my probabilist neighbour François Simenhaus, who immediately pointed out that this probability was more simply seen as the probability that the maximum of N independent geometric rv’s was achieved by a single one among the N. Searching later a reference for that probability, I came across the 1990 paper of Bruss and O’Cinneide, which shows that the probability of uniqueness of the maximum does not converge as N goes to infinity, but rather fluctuates around 0.72135 with logarithmic periodicity. It is only when N=2^n that the sequence converges to 0.721521… This probability actually writes down in closed form as

(which is obvious in retrospect!, albeit containing a typo in the original paper which is missing a ½ factor in equation (17)) and its asymptotic behaviour is not obvious either, as noted by the authors.

On the historical side, and in accordance with Stiegler’s law, the Galton-Watson process should have been called the Bienaymé process! (Bienaymé was a student of Laplace, who successively lost positions for his political idea, before eventually joining Académie des Sciences, and later founding the Société Mathématique de France.)

ISB@CIRM: through the looking glass

It’s now official!, thanks to the support of the Société Mathématique de France (SMF), the Centre National de la Recherche Scientifique (CNRS), and the Université Aix-Marseille, we are going to have a mirror workshop at CIRM, Marseille (France, not South Africa or Ohio!) gathering local Bayesians to attend ISBA 2021 together over the week of 28 June – 2 July, and share more than a virtual meeting room, while increasing the motivation to attend all sessions over a five day ultra-marathon! We also hope to have outdoor poster sessions around breaks.There is no registration fee and no support either, the only cost being the full-board on-site accommodation at CIRM to be paid upon arrival. Registration is open. Until we reach the upper limit set by the centre and depending on the dynamics of the pandemic (and of the administration). So feel free to apply if you are reasonably confident to be allowed and able to reach CIRM on the week of 28 June – 2 July. Which means travelling within the EU, at best.

data assimilation and reduced modelling for high-D problems [CIRM]

Next summer, from 19 July till 27 August, there will be a six week program at CIRM on the above theme, bringing together scientists from both the academic and industrial communities. The program includes a one-week summer school followed by 5 weeks of research sessions on projects proposed by academic and industrial partners.

Confirmed speakers of the summer school (Jul 19-23) are:

• Albert Cohen (Sorbonne University)
• Masoumeh Dashti (University of Sussex)
• Eric Moulines (Ecole Polytechnique)
• Anthony Nouy (Ecole Centrale de Nantes)
• Claudia Schillings (Mannheim University)

Junior participants may apply for fellowships to cover part or the whole stay. Registration and application to fellowships will be open soon.

end-to-end Bayesian learning [CIRM]

Next Fall, there will be a workshop at CIRM, Luminy, Marseilles, on Bayesian learning. It takes place 22-29 October 2021 on this wonderful campus at the border with the beautiful Parc National des Calanques, in a wonderfully renovated CIRM building and involves friends and colleagues of mine as organisers and plenary speakers. (I am not involved!, but plan to organise a scalable MCMC workshop there the year after!) The conference is well-supported and the housing fees will be minimal since the centre is also subsidized by CNRS. The deadline for contributed talks and posters is 22 March, while it is 15 June for registration. Hopefully by this time the horizon will have cleared up enough to consider traveling and meeting again. Hopefully. (In which case I will miss this wonderful conference due to other meeting and teaching commitments in the Fall.)