Special Issue of ACM TOMACS on Monte Carlo Methods in Statistics

As posted here a long, long while ago, following a suggestion from the editor (and North America Cycling Champion!) Pierre Lécuyer (Université de Montréal), Arnaud Doucet (University of Oxford) and myself acted as guest editors for a special issue of ACM TOMACS on Monte Carlo Methods in Statistics. (Coincidentally, I am attending a board meeting for TOMACS tonight in Berlin!) The issue is now ready for publication (next February unless I am confused!) and made of the following papers:

* Massive parallelization of serial inference algorithms for a complex generalized linear model MARC A. SUCHARD, IVAN ZORYCH, PATRICK RYAN, DAVID MADIGAN	Abstract
*Convergence of a Particle-based Approximation of the Block Online Expectation Maximization Algorithm SYLVAIN LE CORFF and GERSENDE FORT	Abstract
* Efficient MCMC for Binomial Logit Models AGNES FUSSL, SYLVIA FRÜHWIRTH-SCHNATTER, RUDOLF FRÜHWIRTH	Abstract
* Adaptive Equi-Energy Sampler: Convergence and Illustration AMANDINE SCHRECK and GERSENDE FORT and ERIC MOULINES	Abstract
* Particle algorithms for optimization on binary spaces CHRISTIAN SCHÄFER	Abstract
* Posterior expectation of regularly paved random histograms RAAZESH SAINUDIIN, GLORIA TENG, JENNIFER HARLOW, and DOMINIC LEE	Abstract
* Small variance estimators for rare event probabilities MICHEL BRONIATOWSKI and VIRGILE CARON	Abstract
* Self-Avoiding Random Dynamics on Integer Complex Systems FIRAS HAMZE, ZIYU WANG, and NANDO DE FREITAS	Abstract
* Bayesian learning of noisy Markov decision processes SUMEETPAL S. SINGH, NICOLAS CHOPIN, and NICK WHITELEY	Abstract

Here is the draft of the editorial that will appear at the beginning of this special issue. (All faults are mine, of course!)

twisted filters

Nick Witheley (Bristol) and Anthony Lee (Warwick) just posted an interesting paper called ‘Twisted particle filters‘ on arXiv. (Presumably unintentionally, the title sounds like Twisted Sister, pictured above, even though I never listened to this [particularly] heavy kind of hard rock! Twisting is customarily used in the large deviation literature.)

The twisted particle paper studies the impact of the choice of something similar to, if subtly different from, an importance function on the approximation of the marginal density (or evidence) for HMMS. (In essence, the standard particle filter is modified for only one particle in the population.) The core of the paper is to compare those importance functions in a fixed N-large n setting. As in simpler importance sampling cases, there exists an optimal if impractical choice of importance function, leading to a zero variance estimator of the evidence. Nick and Anthony produce an upper bound on the general variance as well. One of the most appealing features of the paper is that the authors manage a convergence result in n rather than N. (Although the algorithms are obviously validated in the more standard large N sense.)

The paper is quite theoretical and dense (I was about to write heavy in connection with the above!), with half its length dedicated to proofs. It relies on operator theory, with eigen-functions behind the optimal filter, while not unrelated with Pierre Del Moral’s works. (It took me a while to realise that the notation ω was not the elemental draw from the σ-algebra but rather the realisation of the observed sequence! And I had to keep recalling that θ was the lag operator and not a model parameter [there is no model parameter].)

Course at Monash (#2)

Here are the slides for the second day of my course at Monash University, Melbourne, in the Special Lectures in Econometrics, with a strong strong similarity with the slides of my course in Roma this Spring. (Ah, sunny Roma…) The first day lecture was very well attended and I hope this remains true for the second! (I also think I should spend more time on particle filters in general, the next time I give a similar course…)

MCMC at ICMS (2)

The second day of our workshop on computational statistics at the ICMS started with a terrific talk by Xiao-Li Meng. Although this talk related with his Inception talk in Paris last summer, and of the JCGS discussion paper, he brought new geometric aspects to the phenomenon (managing a zero correlation and hence i.i.d.-ness in the simulation of a Gaussian random effect posterior distribution). While I was reflecting about the difficulty to extend the perspective beyond normal models, he introduced a probit example where exact null correlation cannot be found but an adaptive scheme allows to explore the range of correlation coefficients. This made me somehow think of a possible version in this approach in a tempering perspective, where different data augmentation schemes would be merged into an “optimal” geometric mixture, rather than via interweaving.

As an aside, Xiao-Li mentioned the idea of Bayesian sufficiency and Bayesian ancilarity in the construction of his data augmentation schemes. He then concluded that sufficiency is identical in classical and Bayesian approaches, while ancilarity could be defined in several ways. I have already posted on that, but it seems to me that sufficiency is a weaker notion in the Bayesian perspective in the sense that all that matters is that the posterior is the same given the observation y and given the observed statistics, rather than uniformly over all possible values of the random variable Y as in the classical sense. As for ancilarity, it is also natural to consider that an ancillary statistics does not bring information on the parameter, i.e. that the prior and the posterior distributions are the same given the observed ancillary statistics. Going further to define ancilarity as posterior independence between “true” parameters and auxiliary variables, as Xiao-Li suggested, does not seem very sound as it leads to the paradoxes Basu liked so much!

Today, the overlap with the previous meetings in Bristol and in Banff was again limited: Arnaud Doucet rewrote his talk towards less technicity, which means I got the idea much more clearly than last week. The idea of having a sequence of pseudo-parameters with the same pseudo-prior seems to open a wide range of possible adaptive schemes. Faming Liang also gave a talk fairly similar to the one he presented in Banff. And David van Dyk as well, which led me to think anew about collapsed Gibbs samplers in connection with ABC and a project I just started here in Edinburgh.

Otherwise, the intense schedule of the day saw us through eleven talks. Daniele Impartato called for distributions (in the physics or Laurent Schwarz’ meaning of the term!) to decrease the variance of Monte Carlo estimations, an approach I hope to look further as Schwarz’ book is the first math book I ever bought!, an investment I tried to capitalize once in writing a paper mixing James-Stein estimation and distributions for generalised integration by part, paper that was repeatedly rejected until I gave up! Jim Griffin showed us improvements brought in the exploration of large number of potential covariates in linear and generalised linear models. Natesh Pillai tried to drag us through several of his papers on covariance matrix estimation, although I fear he lost me along the way! Let me perversely blame the schedule (rather than an early rise to run around Arthur’s Seat!) for falling asleep during Alex Beskos’ talk on Hamiltonian MCMC for diffusions, even though I was looking forward this talk. (Apologies to Alex!) Then Simon Byrne gave us a quick tour of differential geometry in connection with orthogonalization for Hamiltonian MCMC. Which brought me back very briefly to this early time I was still considering starting a PhD in differential geometry and then even more briefly played with the idea of mixing differential geometry and statistics à la Shun’ichi  Amari…. Ian Murray and  Simo Sarkka completed the day with a cartoonesque talk on latent Gaussians that connected well with Xiao-Li’s and a talk on Gaussian approximations to diffusions with unknown parameters, which kept within the main theme of the conference, namely inference on partly observed diffusions.

As written above, this was too intense a day, with hardly any free time to discuss about the talks or the ongoing projects, which makes me prefer the pace adopted in Bristol or in Banff. Having to meet a local student on leave from Dauphine for a year here did not help of course!)

Planet Particle Physics [blog aggregator]

I just received an email from Austria that the ‘Og is now part of a blog aggregator, Particle physics planet, along with an impressive list of particle physics blogs. It is certainly an honour to be associated with this blog, even though I fear my random ratiocinations very rarely reach the shore of the particle physics universe…. (I think this is my third “aggregation” after becoming part of R-bloggers and of mathblogging.org)