Particle methods: An introduction with applications

Pierre del Moral (1, 2) , Arnaud Doucet (3)

1 IMB - Institut de Mathématiques de Bordeaux
2 ALEA - Advanced Learning Evolutionary Algorithms
3 Dept of Statistics & Dept of Computer Science

Interacting particle methods are increasingly used to sample from complex high-dimensional distributions. They have found a wide range of applications in applied probability, Bayesian statistics and information engineering. Understanding rigorously these new Monte Carlo simulation tools leads to fascinating mathematics related to Feynman-Kac path integral theory and their interacting particle interpretations. In these lecture notes, we provide a pedagogical introduction to the stochastic modeling and the theoretical analysis of these particle algorithms. We also illustrate these methods through several applications including random walk confinements, particle absorption models, nonlinear filtering, stochastic optimization, combinatorial counting and directed polymer models.

Domaines: Probabilités [math.PR]

Pierre del Moral, Arnaud Doucet. Particle methods: An introduction with applications. [Research Report] RR-6991, INRIA. 2009, pp.46. ⟨inria-00403917⟩