ASPI Research team

Applications of interacting particle systems to statistics

Team presentation

The scientific objectives of the ASPI research project-team are the design, analysis and implementation of interacting Monte Carlo methods, or particle methods, with focus on
  • statistical inference in hidden Markov models, e.g. state or parameter estimation, including particle filtering,
  • risk evaluation, including simulation of rare events.

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,
  • and interact so that only the most successful particles are allowed to survive and to get offsprings at the next generation,
with the effect that this mutation / selection mecanism 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 quantified by the likelihood function. In the most general case, particle methods provide approximations of probability distributions associated with a Feynmac-Kac flow, by means of the weighted empirical probability distribution associated with an interacting particle system.

Research themes

  • particle approximation for linear tangent Feynman-Kac flows, with application to sensitivity analysis,
  • simulation of rare events,
  • simulation-based methods for statistics of hidden Markov models,
  • algorithmic issues.

International and industrial relations

  • industrial projects : with
    • Alcatel Space Industry, on turbo synchronization for satellite communications (terminated),
    • Électricité de France R&D, on calibration of models for electricity price,
  • multi-partner projects : at european level, on
    • conditional Monte Carlo methods for risk assessment (HYBRIDGE / IST),
  • academic research networks : at national level, on
    • hidden Markov chains and particle filtering (HMM-STIC / MathSTIC, terminated),
    • particle methods (AS67 / AS-STIC),
    and at european level, on
    • system identification (ERNSI / TMR, terminated),
    • statistical methods for dynamical stochastic models (DYNSTOCH / IHP).

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

Research teams of the same theme :

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