An Introduction to Sequential Monte Carlo

✍ Scribed by Nicolas Chopin, Omiros Papaspiliopoulos

• Publisher: Springer International Publishing;Springer
• Year: 2020
• Tongue: English
• Leaves: 390
• Series: Springer Series in Statistics
• Edition: 1st ed.
• Category: Library

✦ Synopsis

This book provides a general introduction to Sequential Monte Carlo (SMC) methods, also known as particle filters. These methods have become a staple for the sequential analysis of data in such diverse fields as signal processing, epidemiology, machine learning, population ecology, quantitative finance, and robotics.

The coverage is comprehensive, ranging from the underlying theory to computational implementation, methodology, and diverse applications in various areas of science. This is achieved by describing SMC algorithms as particular cases of a general framework, which involves concepts such as Feynman-Kac distributions, and tools such as importance sampling and resampling. This general framework is used consistently throughout the book.

Extensive coverage is provided on sequential learning (filtering, smoothing) of state-space (hidden Markov) models, as this remains an important application of SMC methods. More recent applications, such as parameter estimation of these models (through e.g. particle Markov chain Monte Carlo techniques) and the simulation of challenging probability distributions (in e.g. Bayesian inference or rare-event problems), are also discussed.

The book may be used either as a graduate text on Sequential Monte Carlo methods and state-space modeling, or as a general reference work on the area. Each chapter includes a set of exercises for self-study, a comprehensive bibliography, and a “Python corner,” which discusses the practical implementation of the methods covered. In addition, the book comes with an open source Python library, which implements all the algorithms described in the book, and contains all the programs that were used to perform the numerical experiments.

✦ Table of Contents

Front Matter ....Pages i-xxiv
Preface (Nicolas Chopin, Omiros Papaspiliopoulos)....Pages 1-10
Introduction to State-Space Models (Nicolas Chopin, Omiros Papaspiliopoulos)....Pages 11-25
Beyond State-Space Models (Nicolas Chopin, Omiros Papaspiliopoulos)....Pages 27-34
Introduction to Markov Processes (Nicolas Chopin, Omiros Papaspiliopoulos)....Pages 35-49
Feynman-Kac Models: Definition, Properties and Recursions (Nicolas Chopin, Omiros Papaspiliopoulos)....Pages 51-65
Finite State-Spaces and Hidden Markov Models (Nicolas Chopin, Omiros Papaspiliopoulos)....Pages 67-71
Linear-Gaussian State-Space Models (Nicolas Chopin, Omiros Papaspiliopoulos)....Pages 73-80
Importance Sampling (Nicolas Chopin, Omiros Papaspiliopoulos)....Pages 81-103
Importance Resampling (Nicolas Chopin, Omiros Papaspiliopoulos)....Pages 105-127
Particle Filtering (Nicolas Chopin, Omiros Papaspiliopoulos)....Pages 129-165
Convergence and Stability of Particle Filters (Nicolas Chopin, Omiros Papaspiliopoulos)....Pages 167-188
Particle Smoothing (Nicolas Chopin, Omiros Papaspiliopoulos)....Pages 189-227
Sequential Quasi-Monte Carlo (Nicolas Chopin, Omiros Papaspiliopoulos)....Pages 229-249
Maximum Likelihood Estimation of State-Space Models (Nicolas Chopin, Omiros Papaspiliopoulos)....Pages 251-277
Markov Chain Monte Carlo (Nicolas Chopin, Omiros Papaspiliopoulos)....Pages 279-291
Bayesian Estimation of State-Space Models and Particle MCMC (Nicolas Chopin, Omiros Papaspiliopoulos)....Pages 293-328
SMC Samplers (Nicolas Chopin, Omiros Papaspiliopoulos)....Pages 329-355
SMC2, Sequential Inference in State-Space Models (Nicolas Chopin, Omiros Papaspiliopoulos)....Pages 357-370
Advanced Topics and Open Problems (Nicolas Chopin, Omiros Papaspiliopoulos)....Pages 371-376
Back Matter ....Pages 377-378

✦ Subjects

Statistics; Statistical Theory and Methods; Big Data; Data-driven Science, Modeling and Theory Building; Statistics and Computing/Statistics Programs; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences