Geodesic
Particle methods: An introduction with applications
Piere Del Moral1 ; Arnaud Doucet2
1 Centre INRIA Bordeaux et Sud-Ouest & Institut de Mathématiques de Bordeaux , Université de Bordeaux I, 351 cours de la Libération 33405 Talence cedex, France,
2 Department of Statistics, Oxford University, 
ESAIM. Proceedings, Tome 44 (2014), pp. 1-46.

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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.
DOI : 10.1051/proc/201444001

Piere Del Moral 1 ; Arnaud Doucet 2

1 Centre INRIA Bordeaux et Sud-Ouest & Institut de Mathématiques de Bordeaux , Université de Bordeaux I, 351 cours de la Libération 33405 Talence cedex, France,
2 Department of Statistics, Oxford University,  
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Piere Del Moral; Arnaud Doucet. Particle methods: An introduction with applications. ESAIM. Proceedings, Tome 44 (2014), pp. 1-46. doi : 10.1051/proc/201444001. http://geodesic.mathdoc.fr/articles/10.1051/proc/201444001/

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