Pierre Del Moral is Research Director at INRIA in France since 2007. He has previously worked at the University of New South Wales (Sydney, Australia); Polytechnique School in Palaiseau, Paris; Laboratoire J. A. Dieudonne of the University of Nice and Sophia-Antipolis; CNRS research fellow at University Paul Sabatier in Toulouse; Ecole Nationale Superieure de l’Aeronautique et de l’Espace in Toulouse; and for the company Steria-Digilog, working on particle filters in tracking problems arising in radar and sonar signal processing problems. He obtained his PhD in 1994 in signal processing with one of the first rigorous study on stochastic particle methods in nonlinear filtering and optimal control problems. His main research interests include branching processes and particle methods, Feynman–Kac formulae, nonlinear filtering, rare event analysis, stochastic algorithms and Markov chain Monte Carlo methodologies. He serves as associate editor for several journals, and has authored several books, including two research monographs, Mean field simulation for Monte Carlo integration and Feynman-Kac formulae: Genealogical and interacting particle approximations, and co-authored Stochastic processes, from applications to theory (with S. Penev).

Pierre’s Medallion Lecture will be delivered at the World Congress in Toronto in July 2016.

An introduction to mean field particle methods

In the last three decades, there has been a dramatic increase in the use of Feynman–Kac type particle methods as a powerful tool in real-world applications of Monte Carlo simulation in computational physics, population biology, computer sciences, and statistical machine learning. The particle simulation techniques they suggest are also called resampled and diffusion Monte Carlo methods in quantum physics, genetic and evolutionary type algorithms in computer sciences, as well as Sequential Monte Carlo methods in Bayesian statistics, and particle filters in advanced signal processing. These mean field type particle methodologies are used to approximate a flow of probability measures with an increasing level of complexity. This class of probabilistic models includes conditional distributions of signals with respect to noisy and partial observations, non-absorption probabilities in Feynman–Kac–Schrödinger type models, Boltzmann–Gibbs measures, as well as conditional distributions of stochastic processes in critical regimes, including quasi-invariant measures and ground state computations.

This lecture presents an introduction to the stochastic modeling and theoretical analysis of these sophisticated probabilistic models. We shall discuss the origins and mathematical foundations of these particle stochastic methods, and applications in rare event analysis, signal processing, mathematical finance and Bayesian statistical inference. We illustrate these methods through several applications: random walk confinements, particle absorption models, nonlinear filtering, stochastic optimization, combinatorial counting and directed polymer models.