Monte Carlo strategies in scientific computing.

*(English)*Zbl 0991.65001
Springer Series in Statistics. New York, NY: Springer. xvi, 343 p. DM 149.69; sFr 128.94; £51.50; $ 69.95 (2001).

This recent addition to the Monte Carlo literature is divided into 13 chapters and an Appendix. It provides both the methodology and the underlying theory for applying Monte Carlo techniques to a broad range of problems.

After a short discussion (Chapters 1 and 2) covering basic Monte Carlo techniques (including the exact sampling method for chain-structured models), the author moves (Chapters 3 and 4) to more advanced subjects as sequential Monte Carlo and its use in different applied fields as molecular simulation, population genetics, computational biology, Bayesian missing data problems, and signal processing problems.

In the next chapters the author focuses his attention on Markov chain based dynamic Monte Carlo strategies: the Metropolis algorithm (Chapter 5), the Gibbs sampler (Chapter 6), cluster algorithms for the Ising model (Chapter 7), conditional sampling (Chapter 8), molecular dynamics and the method of hybrid Monte Carlo (Chapter 9), efficient Monte Carlo sampling (Chapters 10 and 11), Markov chains and their convergence (Chapter 12).

At the end of the book (Chapter 13) the author discusses some theoretical topics related to MCMC. In the Appendix the author outlines the basics in probability theory and statistical inference procedures.

As indicated by the author, this book is intended to serve three audiences: researchers specializing in the study of Monte Carlo algorithms, scientists who are interested in using advanced Monte Carlo techniques, and graduate students in statistics, computational biology, and computer sciences who want to learn about Monte Carlo computations. Overall, this book is a valuable and recommended reference to Monte Carlo methods; particularly it draws the attention to recent work in sequential Monte Carlo.

After a short discussion (Chapters 1 and 2) covering basic Monte Carlo techniques (including the exact sampling method for chain-structured models), the author moves (Chapters 3 and 4) to more advanced subjects as sequential Monte Carlo and its use in different applied fields as molecular simulation, population genetics, computational biology, Bayesian missing data problems, and signal processing problems.

In the next chapters the author focuses his attention on Markov chain based dynamic Monte Carlo strategies: the Metropolis algorithm (Chapter 5), the Gibbs sampler (Chapter 6), cluster algorithms for the Ising model (Chapter 7), conditional sampling (Chapter 8), molecular dynamics and the method of hybrid Monte Carlo (Chapter 9), efficient Monte Carlo sampling (Chapters 10 and 11), Markov chains and their convergence (Chapter 12).

At the end of the book (Chapter 13) the author discusses some theoretical topics related to MCMC. In the Appendix the author outlines the basics in probability theory and statistical inference procedures.

As indicated by the author, this book is intended to serve three audiences: researchers specializing in the study of Monte Carlo algorithms, scientists who are interested in using advanced Monte Carlo techniques, and graduate students in statistics, computational biology, and computer sciences who want to learn about Monte Carlo computations. Overall, this book is a valuable and recommended reference to Monte Carlo methods; particularly it draws the attention to recent work in sequential Monte Carlo.

Reviewer: Radu Theodorescu (Quebec)

##### MSC:

65C05 | Monte Carlo methods |

65C40 | Numerical analysis or methods applied to Markov chains |

60J22 | Computational methods in Markov chains |

62D05 | Sampling theory, sample surveys |

65-02 | Research exposition (monographs, survey articles) pertaining to numerical analysis |

65C60 | Computational problems in statistics (MSC2010) |

82C22 | Interacting particle systems in time-dependent statistical mechanics |

92D25 | Population dynamics (general) |

94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |