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基本説明
New in paperback. Hardcover was published in 2001. Provides a self-contained and up-to-date treatment of the Monte Carlo method and develops a common framework under which various Monte Carlo techniques can be "standardized" and compared.
Full Description
This book provides a self-contained and up-to-date treatment of the Monte Carlo method and develops a common framework under which various Monte Carlo techniques can be "standardized" and compared. Given the interdisciplinary nature of the topics and a moderate prerequisite for the reader, this book should be of interest to a broad audience of quantitative researchers such as computational biologists, computer scientists, econometricians, engineers, probabilists, and statisticians. It can also be used as a textbook for a graduate-level course on Monte Carlo methods.
Contents
1 Introduction and Examples.- 2 Basic Principles: Rejection, Weighting, and Others.- 3 Theory of Sequential Monte Carlo.- 4 Sequential Monte Carlo in Action.- 5 Metropolis Algorithm and Beyond.- 6 The Gibbs Sampler.- 7 Cluster Algorithms for the Ising Model.- 8 General Conditional Sampling.- 9 Molecular Dynamics and Hybrid Monte Carlo.- 10 Multilevel Sampling and Optimization Methods.- 11 Population-Based Monte Carlo Methods.- 12 Markov Chains and Their Convergence.- 13 Selected Theoretical Topics.- A Basics in Probability and Statistics.- A.1 Basic Probability Theory.- A.1.1 Experiments, events, and probability.- A.1.2 Univariate random variables and their properties.- A.1.3 Multivariate random variable.- A.1.4 Convergence of random variables.- A.2 Statistical Modeling and Inference.- A.2.1 Parametric statistical modeling.- A.2.2 Frequentist approach to statistical inference.- A.2.3 Bayesian methodology.- A.3 Bayes Procedure and Missing Data Formalism.- A.3.1 The joint and posterior distributions.- A.3.2 The missing data problem.- A.4 The Expectation-Maximization Algorithm.- References.- Author Index.
