**I**n connection with the recent PhD thesis defence of Juliette Chevallier, in which I took a somewhat virtual part for being physically in Warwick, I read a paper she wrote with Stéphanie Allassonnière on stochastic approximation versions of the EM algorithm. Computing the MAP estimator can be done via some adapted for simulated annealing versions of EM, possibly using MCMC as for instance in the Monolix software and its MCMC-SAEM algorithm. Where SA stands sometimes for stochastic approximation and sometimes for simulated annealing, originally developed by Gilles Celeux and Jean Diebolt, then reframed by Marc Lavielle and Eric Moulines [friends and coauthors]. With an MCMC step because the simulation of the latent variables involves an untractable normalising constant. (Contrary to this paper, Umberto Picchini and Adeline Samson proposed in 2015 a genuine ABC version of this approach, paper that I thought I missed—although I now remember discussing it with Adeline at JSM in Seattle—, ABC is used as a substitute for the conditional distribution of the latent variables given data and parameter. To be used as a substitute for the Q step of the (SA)EM algorithm. One more approximation step and one more simulation step and we would reach a form of ABC-Gibbs!) In this version, there are very few assumptions made on the approximation sequence, except that it converges with the iteration index to the true distribution (for a fixed observed sample) if convergence of ABC-SAEM is to happen. The paper takes as an illustrative sequence a collection of tempered versions of the true conditionals, but this is quite formal as I cannot fathom a feasible simulation from the tempered version and not from the untempered one. It is thus much more a version of tempered SAEM than truly connected with ABC (although a genuine ABC-EM version could be envisioned).

## Archive for École Polytechnique

## ABC-SAEM

Posted in Books, Statistics, University life with tags ABC, ABC-Gibbs, ABC-MCMC, Alan Turing, École Polytechnique, EM, JSM 2015, MAP estimators, MCMC, MCMC-SAEM, Monolix, Paris-Saclay campus, PhD thesis, SAEM, Seattle, simulated annealing, stochastic approximation, University of Warwick, well-tempered algorithm on October 8, 2019 by xi'an## data science summer school à l’X

Posted in Statistics with tags 2019, École Polytechnique, DS3, Paris-Saclay campus, summer school, Université Paris-Saclay, X on January 10, 2019 by xi'an## bâtiment Alan Turing [jatp]

Posted in pictures, Travel, University life with tags Alan Turing, École Polytechnique, INRIA, jatp, Paris-Saclay campus, sculpture on June 24, 2018 by xi'an## [ex?] Paris-Saclay univerXity

Posted in Kids, pictures, University life with tags École Polytechnique, French politics, grandes écoles, Le Monde, MIT, Orsay, Paris-Saclay campus, student association, Université Paris 11, X on November 5, 2017 by xi'an**I**n the plane to Warwick last Tuesday, I read a fairly long and pessimistic article in Le Monde about the future of the Paris-Saclay university. This debate presumably makes no sense outside French circles, for it relates to the century-old opposition between universities and grandes écoles, these selective engineering and business schools that operate independently from the university structure. In the sense that the selection and the schooling of their students is completely separated, meaning these students may never attend a university program if they choose to do so. But not so independently in terms of hiring part-time professors from universities and sharing resources for their Master programs. And depending on the same agencies (like CNRS) for funding their research program.

Anyway, the core message of this article was that the influence of former students from Polytechnique [aka X] in the high administration is such that they can prevent the integration of the different engineer schools on the Saclay plateau into the intended superstructure of the Paris-Saclay university. And turn this somewhat megalomanic Paris-Saclay project initiated by Nicolas Sarkozy into a mere geographical superposition of separate institutions, with very unequal State funding, perpetuating the two speed regime for public higher education… And a ever more confusing international image that will not help an inch moving up the Shanghai ranking (a major reason for Sarkozy pushing this project). Very French indeed!

## a position served on a plate [ENSAE ParisTech, France]

Posted in Kids, pictures, Statistics, Travel, University life with tags academic position, École Polytechnique, ENSAE, France, lost in translation, Paris-Saclay campus, ParisTech, positions, professor of statistics, Saclay, translation on October 6, 2017 by xi'an**N**icolas Chopin emailed me about the opening of a position of Professor of Statistics at [my alma mater] ENSAE, on the Paris-Saclay campus [and plateau], next to Polytechnique, Telecom, and a bunch of other engineer schools [a.k.a The French MIT!]. The largest concentration of Science majors in France, definitely to be considered for a posiiton in France! Deadline is quite soon, as November 1. [Pardon my French: The pun in the title sort of fizzled out in translation because served on a plate is equivalent to served on a plateau in French.]

## Hamiltonian MC on discrete spaces

Posted in Statistics, Travel, University life with tags École Polytechnique, BNP11, capture-recapture, ergodicity, Hamiltonian Monte Carlo, Jolly-Seber model, Laplace distribution, Montréal, open population on July 3, 2017 by xi'an**F**ollowing a lively discussion with Akihiko Nishimura during a BNP11 poster session last Tuesday, I took the opportunity of the flight to Montréal to read through the arXived paper (written jointly with David Dunson and Jianfeng Liu). The issue is thus one of handling discrete valued parameters in Hamiltonian Monte Carlo. The basic “trick” in handling this complexity goes by turning the discrete support via the inclusion of an auxiliary continuous variable whose discretisation is the discrete parameter, hence resembling to some extent the slice sampler. This removes the discreteness blockage but creates another difficulty, namely handling a discontinuous target density. (I idly wonder why the trick cannot be iterated to second or higher order so that to achieve the right amount of smoothness. Of course, the maths behind would be less cool!) The extension of the Hamiltonian to this setting by a convolution is a trick I had not seen since the derivation of the Central Limit Theorem during Neveu’s course at Polytechnique. What I find most exciting in the resolution is the move from a Gaussian momentum to a Laplace momentum, for the reason that I always wondered at alternatives [without trying anything myself!]. The Laplace version is indeed most appropriate here in that it avoids a computation of all discontinuity points and associated values along a trajectory. Since the moves are done component-wise, the method has a Metropolis-within-Gibbs flavour, which actually happens to be a special case. What is also striking is that the approach is both rejection-free and exact, provided ergodicity occurs, which is the case when the stepsize is random.

In addition to this resolution of the discrete parameter problem, the paper presents the further appeal of (re-)running an analysis of the Jolly-Seber capture-recapture model. Where the discrete parameter is the latent number of live animals [or whatever] in the system at any observed time. (Which we cover in Bayesian essentials with R as a neat entry to both dynamic and latent variable models.) I would have liked to see a comparison with the completion approach of Jérôme Dupuis (1995, Biometrika), since I figure the Metropolis version implemented here differs from Jérôme’s. The second example is built on Bissiri et al. (2016) surrogate likelihood (discussed earlier here) and Chopin and Ridgway (2017) catalogue of solutions for not analysing the Pima Indian dataset. (Replaced by another dataset here.)

## end of a long era [1982-2017]

Posted in Books, pictures, Running, University life with tags École Polytechnique, badge, boxes, CREST, ENSAE, INSEE, Insee Paris Club, Malakoff, moving, office, Paris, Paris-Saclay campus on May 23, 2017 by xi'an**T**his afternoon I went to CREST to empty my office there from books and a few papers (like the original manuscript version of Monte Carlo Statistical Methods). This is because the research centre, along with the ENSAE graduate school (my Alma mater), is moving to a new building on the Saclay plateau, next to École Polytechnique. As part of this ambitious migration of engineering schools from downtown Paris to a brand new campus there. Without getting sentimental about this move, it means leaving the INSEE building in Malakoff, on the outskirts of downtown Paris, which has been an enjoyable part of my student and then academic life from 1982 till now. And also leaving the INSEE Paris Club runners! (I am quite uncertain about being as active at the new location, if only because going there by bike is a bit more of a challenge. To be addressed anyway!) And I left behind my accumulation of conference badges (although I should try to recycle them for the incoming BNP 11 in Paris!).