Archive for Randal Douc

Kick-Kac teleportation

Posted in Books, pictures, Statistics with tags , , , , , , , , on January 23, 2022 by xi'an

Randal Douc, Alain Durmus, Aurélien Enfroy, and Jimmy Olson have arXived their Kick-Kac teleportation paper, which was presented by Randal at CIRM last semester. It is based on Kac’s theorem, which states that, for a Markov chain with invariant distribution π, under (π) stationarity, the average tour between two visits to an accessible set C is also stationary. Which can be used for approximating π(h) if π(C) is known (or well-estimated). Jim Hobert and I exploited this theorem in our 2004 perfect sampling paper. The current paper contains a novel proof of the theorem under weaker conditions. (Note that the only condition on C is that it is accessible, rather than a small set. Which becomes necessary for geometric ergodicity, see condition (A4).)

What they define as the Kick-Kac teleportation (KKT) process is the collection of trajectories between two visits to C. Their memoryless version requires perfect simulations from π restricted to the set C. With a natural extension based on a Markov kernel keeping π restricted to the set C stationary. And a further generalisation allowing for lighter tails that also contains the 2005 paper by Brockwell and Kadane as a special case.

The ability of generating from a different kernel Q at each visit to C allows for different dynamics (as in other composite kernels). In their illustrations, the authors use lowest density regions for C, which is rather surprising to me. Except that it allows for a better connection between modes of the target π: the higher performances of the KKT algorithms against the considered alternatives are apparently dependent on the ability of the kernel Q to explore other modes with sufficient frequency.

probabilistic methods in computational statistics [workshop]

Posted in pictures, Statistics, Travel, University life with tags , , , , , , , , , on November 5, 2019 by xi'an

A  one-day workshop is organised at Telecom Sudparis, Évry, on 22 November by R. Douc, F. Portier and F. Roueff. On the “hot topics” concerned with probabilistic methods in computational statistics. The workshop is funded by the project “Big-Pomm”, which strengthens the links between LTCI (Telecom Paristech) and SAMOVAR (Telecom Sudparis) around research projects implying partially observed Markov models. The participation to the workshop is free but registration is required for having access to the lunch buffet (40 participants max). (Évry is located 20km south of Paris, with trains on the RER C line.)

Markov Chains [not a book review]

Posted in Books, pictures, Statistics, University life with tags , , , , , , , , , , , , , on January 14, 2019 by xi'an

As Randal Douc and Éric Moulines are both very close friends and two authors of this book on Markov chains,  I cannot engage into a regular book review! Judging from the table of contents, the coverage is not too dissimilar to the now classic Markov chain Stochastic Stability book by Sean Meyn and the late Richard Tweedie (1994), called the Bible of Markov chains by Peter Glynn, with more emphasis on convergence matters and a more mathematical perspective. The 757 pages book also includes a massive appendix on maths and probability background. As indicated in the preface, “the reason [the authors] thought it would be useful to write a new book is to survey some of the developments made during the 25 years that have elapsed since the publication of Meyn and Tweedie (1993b).” Connecting with the theoretical developments brought by MCMC methods. Like subgeometric rates of convergence to stationarity, sample paths, limit theorems, and concentration inequalities. The book also reflects on the numerous contributions of the authors to the field. Hence a perfect candidate for teaching Markov chains to mathematically well-prepared. graduate audiences. Congrats to the authors!

Le Chemin [featuring Randal Douc]

Posted in Books, pictures, Statistics, Travel, University life with tags , , , , , on September 17, 2017 by xi'an

My friend and co-author Randal Douc is one of the main actors in the film Le Chemin that came out last week in French cinemas. Taking place in Cambodia and directed by Jeanne Labrune. I have not yet seen the film but will next week as it is scheduled in a nearby cinema (and only six in Paris!)… (Randal was also a main actor in Rithy Panh’s Un barrage contre le Pacifique, as well as the off-voice in the Oscar nominated Rithy Panh’s L’image manquante.) In connection with this new movie, Randal was interviewed in Allociné, the major French website on current movies. With questions about his future film and theatre projects, but none about his on-going maths research!!!

Takaisin helsinkiin

Posted in pictures, Statistics, Travel with tags , , , , , , , , , , on July 23, 2017 by xi'an

I am off tomorrow morning to Helsinki for the European Meeting of Statisticians (EMS 2017). Where I will talk on how to handle multiple estimators in Monte Carlo settings (although I have not made enough progress in this direction to include anything truly novel in the talk!) Here are the slides:

I look forward this meeting, as I remember quite fondly the previous one I attended in Budapest. Which was of the highest quality in terms of talks and interactions. (I also remember working hard with Randal Douc on a yet-unfinished project!)

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