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ASPI Research team

Applications of interacting particle systems to statistics

  • Leader : François Le gland
  • Research center(s) : CRI Rennes - Bretagne Atlantique
  • Field : Applied Mathematics, Computation and Simulation
  • Theme : Stochastic approaches
  • Partner(s) : Université Rennes 1,Université Haute Bretagne (Rennes 2),CNRS
  • Collaborator(s) : U. RENNES 1, ENS CACHAN, CNRS, INSA RENNES, U. RENNES 2

Team presentation

The scientific objectives of ASPI are the design, analysis and implementation of interacting Monte Carlo methods, or particle methods, or sequential Monte Carlo (SMC) methods, dedicated to

  • statistical inference in partially observed Markov models and particle filtering,
  • risk evaluation and simulation of rare events.

ASPI carries methodological research activities, so as to obtain generic results, with techniques borrowed to the many scientific areas that have contributed to the field (interacting particle systems, empirical processes, genetic algorithms (GA), hidden Markov models (HMM) and nonlinear filtering, Bayesian statistics, Markov chain Monte Carlo (MCMC) methods, etc.), and implements these techniques and results on some appropriate examples, through collaborations with industrial and academic partners.

Scientific background

Intuitively speaking, interacting Monte Carlo methods are sequential simulation methods, in which particles

  • explore the state space by mimicking the evolution of an underlying random process,
  • learn their environment by evaluating a fitness function,
  • and interact so that only the most successful / fit particles are allowed to survive and to get offsprings at the next generation.

The effect that this mutation / selection mecanism is to automatically concentrates particles (i.e. the available computing power) in regions of interest of the state space. In the special case of particle filtering, which has numerous applications in positioning, navigation and tracking, visual tracking, mobile robotics, etc., each particle represents a possible hidden state, and is multiplied or terminated at the next generation on the basis of its consistency with the current observation, as measured by the likelihood function. In the most general case, particle methods provide efficient approximations of Feynmac-Kac distributions, by means of the weighted empirical probability distribution associated with an interacting particle system, with applications that go far beyond filtering, in simulation of rare events, black-box optimization, molecular simulation, etc.

Research themes

  • algorithmic issues : regularization, adaptive redistribution, Rao-Blackwellization, non-extinction of particle system, approximate Bayesian computation (ABC),
  • simulation of rare events : importance splitting / sampling, RESTART algorithm,
  • Feynman-Kac distributions depending on a parameter (application to sensitivity analysis) : smooth particle approximation, particle approximation of linear tangent distribution,
  • statistical inference of partially observed Markov models : asymptotic behavior (connection with stability of the Bayesian filter), simulation-based methods,
  • sequential data assimilation : ensemble Kalman filter (EnKF) vs. particle filters, Monte Carlo methods in high dimension.

International and industrial relations

  • industrial projects, with
    • DCNS, on track-before-detect for multiple targets,
    • CEA/LETI, on particle filtering for indoor navigation,
    • DGA Techniques navales (ex-DGA/CTSN), on optimization of sensors location and activation,
    • Thalès Communications (project NCT, DGA), on terrain-aided navigation,
    • France Télécom R&D, on positioning and tracking mobile terminals,
    • Électricité de France R&D, on calibration of models for electricity price,
  • european projects
    • iFLY (programme Aeronautics and Space, FP6), on safety based design and validation of highly automated air traffic management,
    • HYBRIDGE (programme IST, FP5), on distributed control and stochastic analysis of hybrid systems,
  • national research networks
    • SEACS (inter Labex CominLabs, Henri Lebesgue, Mer), on stochastic representation of geophysical fluids coupling dynamical models and massive data,
    • COSMOS (challenge Information and Communication Society, ANR), on computational statistics and molecular simulation,
    • GERONIMO (programme JCJC, ANR), on geophysical reduced-order models from image observations,
    • PIECE (programme JCJC, ANR), on piecewise-deterministic Markov processes,
    • PREVASSEMBLE (programme Conception and Simulation, ANR), on ensemble methods for prediction and data assimilation,
    • FIL (programme Telecommunications, ANR), on information fusion for localisation,
    • NEBBIANO (programme SETIN, ANR), on security and reliability in digital watermarking,
    • RARE (programme ARC, INRIA), on analysis of rare events using Monte Carlo methods,
    • ADOQA (programme ARC, INRIA), on data assimilation for air quality,
    • AS67 (programme AS-STIC, CNRS), on particle methods,
    • HMM-STIC (programme MathSTIC, CNRS), on hidden Markov chains and particle filtering,
  • european research networks
    • DYNSTOCH (programme IHP, FP5), on statistical methods for dynamical stochastic models,
    • ERNSI (programme TMR), on system identification.

Keywords: Particle filtering Monte Carlo method Interacting particle system Statistical inference Hidden Markov model Positioning Navigation Tracking Rare event Risk assessment