Archive for MCQMC2014

MCqMC 2014 [day #3]

Posted in pictures, Running, Statistics, Travel, University life, Wines with tags , , , , , , , , , , , , , , , , on April 10, 2014 by xi'an

Leuven2

As the second day at MCqMC 2014, was mostly on multi-level Monte Carlo and quasi-Monte Carlo methods, I did not attend many talks but had a long run in the countryside (even saw a pheasant and a heron), worked at “home” on pressing recruiting evaluations and had a long working session with Pierre Jacob. Plus an evening out sampling (just) a few Belgian beers in the shade of the city hall…

Today was more in my ballpark as there were MCMC talks the whole day! The plenary talk was not about MCMC as Erich Novak presented a survey on the many available results bounding the complexity of approximating an integral based on a fixed number of evaluations of the integrand, some involving the dimension (and its curse), some not, some as fast as √n and some not as fast, all this depending on the regularity and the size of the classes of integrands considered. In some cases, the solution was importance sampling, in other cases, quasi-Monte Carlo, and yet other cases were still unsolved. Then Yves Atchadé gave a new perspective on computing the asymptotic variance in the central limit theorem on Markov chains when truncating the autocovariance, Matti Vihola talked about theoretical orderings of Markov chains that transmuted into the very practical consequence that using more simulations in a pseudo-marginal likelihood approximation improved acceptance rate and asymptotic variances (and this applies to aBC-MCMC as well), Radu Craiu proposed a novel processing of adaptive MCMC by treating various approximations to the true target as food for a multiple-try Metropolis algorithm, and Luca Martino had a go at resuscitating the ARMS algorithm of Gilks and Wild (used for a while in BUGS), although the talk did not dissipate all of my misgivings about the multidimensional version! I had more difficulties following the “Warwick session” which was made of four talks by current or former students from Warwick, although I appreciated the complexity of the results in infinite dimensional settings and novel approximations to diffusion based Metropolis algorithms. No further session this afternoon as the “social” activity was to visit the nearby Stella Artois brewery! This activity made us very social, for certain, even though there was hardly a soul around in this massively automated factory. (Maybe an ‘Og post to come one of those days…)

MCqMC 2014 [day #1]

Posted in pictures, Running, Statistics, Travel, University life with tags , , , , , , , , , on April 9, 2014 by xi'an

Leuven2

As I have been kindly invited to give a talk at MCqMC 2014, here am I. in Leuven, Belgium, for this conference I have never attended before. (I was also invited for MCqMC 2012 in Sydney The talk topics and the attendees’ “sociology” are quite similar to those of the IMACS meeting in Annecy last summer. Namely, rather little on MCMC, particle filters, and other tools familiar in Bayesian computational statistics, but a lot on diffusions and stochastic differential equations and of course quasi-Monte Carlo methods. I thus find myself at a boundary of the conference range and a wee bit lost by some talks, which even titles make little sense to me.

For instance, I have trouble to connect with multi-level Monte Carlo within my own referential. My understanding of the method is one of a control variate version of tempering, namely of using a sequence of approximations to the true target and using rougher approximations as control variates for the finer approximations. But I cannot find on the Web a statistical application of the method outside of diffusions and SDEs, i.e. outside of continuous time processes… Maybe using a particle filter from one approximation to the next, down in terms of roughness, could help.

“Several years ago, Giles (2008) introduced an intriguing multi-level idea to deal with such biased settings that can dramatically improve the rate of convergence and can even, in some settings, achieve the canonical “square root” convergence rate associated with unbiased Monte Carlo.” Rhee and Glynn, 2012

Those were my thoughts before lunchtime. today (namely April 7, 2014). And then, after lunch, Peter Glynn gave his plenary talk that just answered those questions of mine’s!!! Essentially, he showed that formula Pierre Jacob also used in his Bernoulli factory paper to transform a converging-biased-into-an-unbiased estimator, based on a telescopic series representation and a random truncation… This approach is described in a paper with Chang-han Rhee, arXived a few years ago. The talk also covered more recent work (presumably related with Chang-han Rhee’s thesis) extending the above to Markov chains. As explained to me later by Pierre Jacob [of Statisfaction fame!], a regular chain does not converge fast enough to compensate for the explosive behaviour of the correction factor, which is why Rhee and Glynn used instead a backward chain, linking to the exact or perfect samplers of the 1990’s (which origin can be related to a 1992 paper of Asmussen, Glynn and Thorisson). This was certainly the most riveting talk I attended in the past years in that it brought a direct answer to a question I was starting to investigate. And more. I was also wondering how connected it was with our “exact” representation of the stationary distribution (in an Annals of Probability paper with Jim Hobert).   Since we use a stopping rule based on renewal and a geometric waiting time, a somewhat empirical version of the inverse probability found in Peter’s talk. This talk also led me to re-consider a recent discussion we had in my CREST office with Andrew about using square root(ed) importance weights, since one of Peter’s slides exhibited those square roots as optimal. Paradoxically, Peter started the talk by down-playing it, stating there was a single idea therein and a single important slide, making it a perfect after-lunch talk: I wish I had actually had thrice more time to examine each slide! (In the afternoon session, Éric Moulines also gave a thought-provoking talk on particle islands and double bootstrap, a research project I will comment in more detail the day it gets arXived.)

Leuven snapshot [#2]

Posted in pictures, Running, Travel with tags , , , on April 8, 2014 by xi'an

Leuven3

Leuven snapshot [#1]

Posted in pictures, Running, Statistics, Travel, University life with tags , , , , on April 7, 2014 by xi'an

Leuven1

MCQMC2014 in Belgium

Posted in Books, Statistics, Travel, University life with tags , , , , , , , , , on October 11, 2013 by xi'an

The conference MCQMC2014 (which stands for Monte Carlo and Quasi-Monte Carlo) will take place in Leuven, Belgium, on April 6-11. More exactly, in the Katholieke Universiteit Leuven, which is the Flemish-speaking side of the split (1968) Catholic University of Leuven, the French speaking side Université Catholique de Louvain being located in Louvain-la-Neuve. After missing MCQMC2012 in Sydney,  I will attend this conference where I give an invited talk (on ABC, what else..?!). As it happens (and kind of logically), I have visited Louvain-la-Neuve many times, especially in the previous era where historical Bayesians Michel Mouchard, Jean-Marie Rolin and Léopold Simar were together in the Statistics department—two of them contributing to the highly formalised “Elements of Bayesian Statistics” that I perused during my PhD thesis in Rouen—, but I have never been to Leuven or to KU Leuven,

A great item of news is that one of the two tutorials (on April 6, 2014) will given by Art Owen, the theme being “ANOVA, global sensitivity, Sobol’ indices and all that“, The second tutorial is by Mike Giles (Oxford) on his approach of multi-level Monte Carlo methods. (If the organisers follow the MCQMC2012 trend, the Sunday afternoon tutorials should follow one another.)

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