科學計算中的蒙特卡羅策略

內(nèi)容概要

An early experiment that conceives the basic idea of Monte Carlo compu-tatios is known as "Buffon'needle",first stated by Georges Louis Leclerc Comte de Buffon in 1777.In this well-known experiment,on throws a needle of length l onto a flat surface with a grid of parallel lines with spacing.It is easy to compute that,under ideal conditions,the chance that the needle will intersect one of the lines in .Thus,if we lep pN be the Proportion of "intersects"in N throws,we can have an estimate of π as wjocj will"converge"to π as N increases to infinity.

書籍目錄

Preface 1 Introduction and Examples 　1.1 The Need of Monte Carlo Techniques 　1.2 Scope and Outline of the Book 　1.3 Computations in Statistical Physics 　1.4 Molecular Structure Simulation 　1.5 Bioinformatics: Finding Weak Repetitive Patterns 　1.6 Nonlinear Dynamic System: Target Tracking 　1.7 Hypothesis Testing for Astronomical Observations 　1.8 Bayesian Inference of Multilevel Models 　1.9 Monte Carlo and Missing Data Problems 2 Basic Principles: Rejection， Weighting， and Others 　2.1 Generating Simple Random Variables 　2.2 The Rejection Method 　2.3 Variance Reduction Methods 　2.4 Exact Methods for Chain-Structured Models 　　2.4.1 Dynamic programming 　　2.4.2 Exact simulation 　2.5 Importance Sampling and Weighted Sample 　　2.5.1 An example 　　2.5.2 The basic idea    2.5.3 The "rule of thumb"for importance sampling……3 Theory of Sequential Monte Carlo4 Sequential Monte Carlo in Action5 Metropolis Algorithm and Beyond6 The Gibbs Sampler7 Cluster Algorithms for the Ising Model8 General Conditionl Sampling9 Molecular Dynamics and Hybrid Monte Carlo10 Multievel Sampling and Optimization Methods11 Population-Based Monte Carlo Methods12 Markov Chains and Their Convergence13 Selected Theoretical TopicsA Basics in Probability and StatisticsReferencesAuthor IndexSubject Index

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