Workshop Filtering, MCMC, ABC

Lille, 28-29 March 2011

Organized by Paul Painlevé Laboratory, LAGIS and LISIC

Ecole Centrale in Lille, Grand Amphi, Villeneuve d'Ascq

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Summary of the workshop       Schedule    Venue     Registration (CLOSED)     Organizing Committee


Summary of the workshop

The aim of this workshop is to give an insight on the research perspectives in Markov Chain Monte Carlo, Approximate Bayesian Filtering and Sequential Monte Carlo Methods. Researchers whose results are references in theses fields will be giving their feeling along the two days of this workshop.


Temporary Schedule

Monday 28th March

We address the problem of upper bounding the mean square error of MCMC estimators. Our analysis is non-asymptotic. We first establish a general result valid for essentially all ergodic Markov chains encountered in Bayesian computation and a  possibly unbounded target function. The bound is sharp in the sense that the leading term is exactly (asymptotic variance)/n,  where "asymptotic variance" is the same as in the Central Limit Theorem. The method of proof is based on regeneration techniques and renewal theory. Next, we proceed to specific assumptions and give explicit computable bounds for
geometrically and polynomially ergodic Markov chains. Main assumption is a (geometric or polynomial) drift condition. As a corollary we provide results on confidence estimation.
Sequential Monte Carlo methods (often termed particle filters in this context) are one of the most versatile computational approaches to the (discrete time) filtering problem. The preliminary work presented develops techniques which allow almost automatic block-sampling in this setting. This approach substantially improving the path-space performance of these algorithms, allowing online inference in settings in which the whole trajectory of the unobserved Markov process is of interest. Results for simple examples illustrate the potential of the proposed approach.
We study approximations of evolving probability measures by an interacting particle system. The particle system dynamics is a combination of independentMarkov chain moves and importance sampling/resampling steps. We study the time evolution of the approximation errors in appropriate Lp norms. Under globalregularity conditions, we derive non-asymptotic Lp error bounds. The main motivationare applications to sequential MCMC methods for Monte Carlo integral estimation.
In this talk we will describe a novel approach to inference in previously intractable alpha-stable stochastic processes. The methods  involve a stochastic series expansion of the alpha-stable Levy-driven process in terms of an infinite summation of Poisson jump arrival times and jump amplitudes, which may be used very effectively in an auxiliary variables Monte Carlo simulation scheme. Examples will be given of  parameter estimation for linear SDEs driven by alpha-stable Levy processes, and also for discrete time autoregressive processes driven by  alpha-stable innovations.

Tuesday 29th March

  Approximate Bayesian computation (ABC) is a class of algorithmic methods in Bayesian inference using statistical summaries and computer simulations. Model selection under ABC algorithms has been a subject of intense debate during the recent years, and several methods have been proposed to approximate model probabilities. Here we show that the simplest and most popular of these methods leads to biased model choice when regression adjustments are further performed on approximate posterior distributions. We propose an alternative to the approximation of model probabilities based on posterior predictive distributions and approximations of the expected deviance. A simulation study shows that the approximate deviance criteria can correctly account for regression adjustments, and lead to sensible results in a number of model choice problems of interest to population geneticists.
We consider the problem of estimating a latent point process, given the realization of another point process on abstract measurable state spaces. First, we establish an expression of the conditional distribution of a latent Poisson point process given the observation process when the transformation from the latent process to the observed process includes displacement, thinning and augmentation with extra points. We present an original analysis based on a self-contained random measure theoretic approach combined with reversed Markov kernel techniques. In the second part, we analyse the exponential stability properties of nonlinear multi-target filtering equations. We prove uniform convergence properties w.r.t. the time parameter of a rather general class of stochastic filtering algorithms, including sequential Monte Carlo type models and mean field particle interpretation models. We illustrate these results in the context of the Bernoulli and the Probability Hypothesis Density filter.
Venue

The workshop will be held at the Ecole Centrale in Lille on the Universitary Domain of Villeneuve d'Ascq (DUSVA) next to the campus of the University of Lille 1 :

ECOLE CENTRALE DE LILLE
Cité Scientifique - BP 48
59651 Villeneuve d'Ascq Cedex

You'll find a map to come here.

The easiest way to come is by subway : line 1 , 4 Canton station.

If you come by car, from the A1 motorway, follow Bruxelles then Villeneuve d'Ascq : Cité Scientifique exit (first exit).




Registration (free but compulsory) : CLOSED

Registration is free of charge but compulsory because we need the number of attendees to organize coffee breaks and to make the reservations at the restaurants for the lunchs and the dinner on Monday evening.

Organizing Committe

Painlevé       LAGIS       LISIC

CNRS       University of Lille 1       EC Lille           Graisyhm   



Summary of the workshop       Schedule    Venue     Registration     Organizing Committee