Mean Field Simulation for Monte Carlo Integration

This book presents the first comprehensive and modern mathematical treatment of these mean field particle models, including refined convergence analysis on nonlinear Markov chain models. It also covers applications related to parameter estimation in hidden Markov chain models, stochastic optimization, nonlinear filtering and multiple target tracking, stochastic optimization, calibration and uncertainty propagations in numerical codes, rare event simulation, financial mathematics, and free energy and quasi-invariant measures arising in computational physics and population biology.

In the last three decades, there has been a dramatic increase in the use of interacting particle methods as a powerful tool in real-world applications of Monte Carlo simulation in computational physics, population biology, computer sciences, and statistical machine learning. Ideally suited to parallel and distributed computation, these advanced particle algorithms include nonlinear interacting jump diffusions; quantum, diffusion, and resampled Monte Carlo methods; Feynman-Kac particle models; genetic and evolutionary algorithms; sequential Monte Carlo methods; adaptive and interacting Markov chain Monte Carlo models; bootstrapping methods; ensemble Kalman filters; and interacting particle filters.

Mean Field Simulation for Monte Carlo Integration presents the first comprehensive and modern mathematical treatment of mean field particle simulation models and interdisciplinary research topics, including interacting jumps and McKean-Vlasov processes, sequential Monte Carlo methodologies, genetic particle algorithms, genealogical tree-based algorithms, and quantum and diffusion Monte Carlo methods.

Along with covering refined convergence analysis on nonlinear Markov chain models, the author discusses applications related to parameter estimation in hidden Markov chain models, stochastic optimization, nonlinear filtering and multiple target tracking, stochastic optimization, calibration and uncertainty propagations in numerical codes, rare event simulation, financial mathematics, and free energy and quasi-invariant measures arising in computational physics and population biology.

This book shows how mean field particle simulation has revolutionized the field of Monte Carlo integration and stochastic algorithms. It will help theoretical probability researchers, applied statisticians, biologists, statistical physicists, and computer scientists work better across their own disciplinary boundaries.

"I found this to be an enjoyable read. Many illustrative examples reveal intriguing paradoxes in statistical theories, some of them are well-known and complemented with a broad informative discussion and others are less obvious."Journal of the American Statistical Association

Autorentext

Pierre Del Moral is a professor in the School of Mathematics and Statistics at the University of New South Wales in Sydney, Australia.

Inhalt

Monte Carlo and Mean Field Models. Theory and Applications. Feynman-Kac Models: Discrete Time Feynman-Kac Models. Four Equivalent Particle Interpretations. Continuous Time Feynman-Kac Models. Nonlinear Evolutions of Intensity Measures. Application Domains: Particle Absorption Models. Signal Processing and Control Systems. Theoretical Aspects: Mean Field Feynman-Kac Models. A General Class of Mean Field Models. Empirical Processes. Feynman-Kac Semigroups. Intensity Measure Semigroups. Particle Density Profiles. Genealogical Tree Models. Particle Normalizing Constants. Backward Particle Markov Models. Bibliography. Index.