×

On the concentration properties of interacting particle processes. (English) Zbl 1280.60057

This monograph presents some new concentration inequalities for Feynman-Kac particle processes. We analyze different types of stochastic particle models, including particle profile occupation measures, genealogical tree based evolution models, particle free energies, as well as backward Markov chain particle models. We illustrate these results with a series of topics related to computational physics and biology, stochastic optimization, signal processing and Bayesian statistics, and many other probabilistic machine learning algorithms. Special emphasis is given to the stochastic modeling, and to the quantitative performance analysis of a series of advanced Monte Carlo methods, including particle filters, genetic type island models, Markov bridge models, and interacting particle Markov chain Monte Carlo methodologies.

MSC:

60K35 Interacting random processes; statistical mechanics type models; percolation theory
65C35 Stochastic particle methods
47D08 Schrödinger and Feynman-Kac semigroups
82C22 Interacting particle systems in time-dependent statistical mechanics
65C05 Monte Carlo methods
62G20 Asymptotic properties of nonparametric inference
60E15 Inequalities; stochastic orderings
PDFBibTeX XMLCite
Full Text: DOI arXiv