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.

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

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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 Conditionl Sampling

9 Molecular Dynamics and Hybrid Monte Carlo

10 Multievel 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

References

Author Index

Subject Index