**I** hesitated in changing the above title for “MCqMSmaug” as the plenary talk I attended this morning was given by Wenzel Jakob, who uses Markov chain Monte Carlo methods in image rendering and light simulation. The talk was low-tech’, with plenty of pictures and animations (incl. excerpts from recent blockbusters!), but it stressed how much proper rending relies on powerful MCMC techniques. One point particularly attracted my attention, namely the notion of manifold exploration as it seemed related to my zero measure recent post. (A related video is available on Jakob’s webpage.) You may then wonder where the connection with Smaug could be found: Wenzel Jakob is listed in the credits of both Hobbit movies for his contributions to the visual effects! (Hey, MCMC made Smaug [visual effects the way they are], a cool argument for selling your next MCMC course! I will for sure include a picture of Smaug in my next R class presentation…) The next sessions of the morning opposed Sobol’s memorial to more technical light rendering and I chose Sobol, esp. because I had missed Art Owen’s tutorial on Sunday, as he gave a short presentation on using Sobol’s criteria to identify variables contributing the most to the variability or extreme values of a function, an extreme value kind of ANOVA, most interesting if far from my simulation area… The afternoon sessions saw MCMC talks by Luke Bornn and Scott Schmidler, both having connection with the Wang-Landau algorithm. Actually, Scott’s talk was the one generating the most animated discussion among all those I attended in MCqMC! (To the point of the chairman getting rather rudely making faces…)

## Archive for Wang-Landau algorithm

## MCqMC 2014 [day #4]

Posted in pictures, Running, Statistics, Travel, University life with tags ANOVA models, Fourier transform, image rendering, manifold exploration, MCMC, MCQMC2014, Riemann manifold, Smaug, Sobol sequences, The Hobbit, Wang-Landau algorithm on April 11, 2014 by xi'an## published in Brazilian Journal of Probability and Statistics, esplêndido!

Posted in Statistics, University life with tags ABC, Brazil, Ising model, untractable normalizing constant, Wang-Landau algorithm on September 24, 2013 by xi'an**O**ur paper “Bayesian computation for statistical models with intractable normalizing constants” written with Yves Atchadé and Nicolas Lartillot has now appeared in the Brazilian Journal of Probability and Statistics! (This is my first paper in this journal.) Although we could have used ABC steps to approximate the posterior, we chose instead a Wang-Landau approach that has exact convergence properties and extends the 1992 Read Paper by Charlie Geyer and Elisabeth Thompson.

## Hamilton confronting intractability (with a li’le help from Metropolis)

Posted in Mountains, pictures, Statistics, Travel, University life with tags bag, Bristol, Edinburgh, England, Glasgow, Hamiltonian Monte Carlo, ICMS, Oxford, Scotland, SuSTain, Wang-Landau algorithm on April 20, 2012 by xi'an**L**ast day of a great workshop! I filled more pages of my black notebook (“bloc”) than in the past month!!! This morning started with an Hamiltonian session, Paul Fearnhead presenting recent developments in this area. I liked his coverage very much, esp. because it went away from the physics analogies that always put me off. The idea of getting away from the quadratic form had always seemed natural to me and provided an interesting range for investigations. (I think I rediscovered the topic during the talks, rephrasing almost the same questions as for Girolami’s and Calderhead’s Read Paper!) One thing that still intrigues me is the temporal dimension of the Hamiltonian representation. Indeed, it is “free” in the sense that the simulation problem does not depend on the time the pair (x,p) is moved along the equipotential curve. (In practice, there is a cost in running this move because it needs to be discretised.) But there is no clear target function to set the time “right”. The only scale I can think of is when the pair comes back by its starting point. Which is less silly than it sounds because the discretisation means that all intermediate points can be used, as suggested by Paul via a multiple try scheme. Mark then presented an application of Hamiltonian ideas and schemes to biochemical dynamics, with a supplementary trick of linearisation. Christian Lorenz Müller gave an ambitious *grand tour* of gradient free optimisation techniques that sounded appealing from a simulation perspective (but would require a few more hours to apprehend!), Geoff Nicholls presented on-going research on approximating Metropolis-Hastings acceptance probabilities in a more general perspective than *à la* Andrieu-Robert, i.e. accepting some amount of bias, an idea he has explained to me when I visited Oxford. And Pierre Jacob concluded the meeting in the right tone with a *pot-pourri* of his papers on Wang-Landau. (Once again a talk I had already heard but that helped me make more sense of a complex notion…)

**O**verall and talk-by-talk, a truly exceptional meeting. Which also set the bar quite high for us to compete at the ICMS meeting on advances in MCM next Monday! Esp. when a portion of the audience in Bristol will appear in Edinburgh as well!an In the meanwhile, I have to rewrite my talk for the seminar in Glasgow tomorrow in order to remove the overlap with my talk there last year… *(I note that I have just managed to fly to Scotland with no lost bag, a true achievement!)*

## Wang, Landau, Markov, and others…

Posted in pictures, Statistics, University life with tags Big' MC, Feynman-Kac formalism, Institut Henri Poincaré, Landau, Markov, particle system, Perron-Frobenius theory, seminar, Wang, Wang-Landau algorithm on April 11, 2012 by xi'an**O**n Thursday, the “Big’MC” seminar welcomes two talks (at 3pm and 4pm, resp., in IHP, Amphi Darboux):

- Orateur :Pierre Jacob (ENSAE) et Robin Ryder (CEREMADE)
- Titre : Some aspects of the Wang-Landau algorithm.
- Résumé : The Wang-Landau algorithm is an adaptive MCMC algorithm which generates a Markov chain designed to move efficiently in the state space, by constantly penalizing already-visited regions. It hence falls into the class of exploratory algorithms, especially when the chosen regions correspond to different levels of density values. We explore two novel aspects of the Wang-Landau algorithm. First, we show that the algorithm reaches the so-called Flat Histogram criterion in finite time, which ensures convergence properties. Second, we examine the effect of using multiple chains, interacting through a common component. That component essentially represents the history of already-visited regions, computed on all the chains. We show numerically the benefit of using parallel chains even if a single processing unit is available, in terms of stabilization of the schedule used in the adaptation process. If time permits, we shall present an ongoing attempt to study theoretically the effect of parallelization using Feynman-Kac semigroups.
- Références http://arxiv.org/abs/1110.4025 et http://arxiv.org/abs/1109.3829

and

- Orateur : Nick Whiteley ( Univ. Bristol, UK)
- Titre : A particle method for approximating principal eigen-functions and related quantities
- Résumé : Perron-Frobenius theory treats the existence of a positive eigen-vector associated with the principal eigen-value \lambda_{\star} of a non-negative matrix, say Q. A simple method for approximating this eigen-vector involves computing the iterate \lambda_{\star}^{-n}Q^{(n)}, for large n. In the more general case that Q is a non-negative integral kernel, an extended Perron-Frobenius theory applies, but it is typical that neither the principal eigen-function nor the iterate \lambda_{\star}^{-n}Q^{(n)} can be computed exactly. In this setting we introduce an interacting particle algorithm which yields a numerical approximation of the principal eigen-function and the associated twisted Markov kernel. Some of its theoretical properties will be discussed and applications will be outlined. In particular, the algorithm allows approximation of an optimal importance sampling method for Markov chain rare event estimation.

Joint work with Nikolas Kantas.

- Référence : http://arxiv.org/abs/1202.6678

## English trip (1)

Posted in Statistics, Travel, University life with tags ABC, Cambridge University, CRiSM, Edinburgh, GPU, graphics processing units, Kenilworth, model choice, parallel processing, Scotland, University of Oxford, University of Warwick, Wang-Landau algorithm, Warwick on January 25, 2012 by xi'an**T**oday, I am attending a workshop on the use of graphics processing units in Statistics in Warwick, supported by CRiSM, presenting our recent works with Randal Douc, Pierre Jacob and Murray Smith. (I will use the same slides as in Telecom two months ago, hopefully avoiding the loss of integral and summation signs this time!) Pierre Jacob will talk about Wang-Landau.

**T**hen, tomorrow, I am off to Cambridge to talk about ABC and model choice on Friday afternoon. (Presumably using the same slides as in Provo.)

*The (1) in the title is in prevision of a second trip to Oxford next month and another one to Bristol two months after! (The trip to Edinburgh does not count of course, since it is in Scotland!)
*