It is a tribute to our profession that a textbook that was current in 1999 is starting to feel old. The work for the first edition of Monte Carlo Statistical Methods (MCSM1) was finished in late 1998, and the advances made since then, as well as our level of understanding of Monte Carlo methods, have grown a great deal. Moreover, two other things have happened. Topics that just made it into MCSM1 with the briefest treatment (for example, perfect sampling) have now attained a level of importance that necessitates a much more thorough treatment. Secondly, some other methods have not withstood the test of time or, perhaps, have not yet been fully developed, and now receive a more appropriate treatment.
When we worked on MCSM1 in the mid-to-late 90s, MCMC algorithms were already heavily used, and the flow of publications on this topic was atsuch a high level that the picture was not only rapidly changing, but also necessarily incomplete. Thus, the process that we followed in MCSM1 was that of someone who was thrown into the ocean and was trying to grab onto the biggest and most seemingly useful objects while trying to separate the flotsam from the jetsam. Nonetheless, we also felt that the fundamentals of many of these algorithms were clear enough to be covered at the textbook alevel, so we" swam on.
Preface to the Second Edition
Preface to the First Edition
1 Introduction
1.1 Statistical Models
1.2 Likelihood Methods
1.3 Bayesian Methods
1.4 Deterministic Numerical Methods
1.4.1 Optimization
1.4.2 Integration
1.4.3 Comparison
1.5 Problems
1.6 Notes
1.6.1 Prior Distributions
1.6.2 Bootstrap Methods
2 Random Variable Generation
2.1 Introduction
2.1.1 Uniform Simulation
2.1.2 The Inverse Transform
2.1.3 Alternatives
2.1.4 Optimal Algorithms
2.2 General Transformation Methods
2.3 Accept Reject Methods
2.3.1 The Fundamental Theorem of Simulation
2.3.2 The Accept-Reject Algorithm.
2.4 Envelope Accept Reject Methods
2.4.1 The Squeeze Principle
2.4.2 Log-Concave Densities
2.5 Problems
2.6 Notes
2.6.1 The Kiss Generator
2.6.2 Quasi-Monte Carlo Methods
2.6.3 Mixture Representations
3 Monte Carlo Integration
3.1 Introduction
3.2 Classical Monte Carlo Integration
3.3 Importance Sampling
3.3.1 Principles
3.3.2 Finite Variance Estimators
3.3.3 Comparing Importance Sampling with Accept-Reject
3.4 Laplace Approximations
3.5 Problems
3.6 Notes
3.6.1 Large Deviations Techniques
3.6.2 The Saddlepoint Approximation
4 Controling Monte Carlo Variance
4.1 Monitoring Variation with the CLT
4.1.1 Univariate Monitoring
4.1.2 Multivariate Monitoring
4.2 Rao-Blackwellization
4.3 RieInann Approximations
4.4 Acceleration Methods
4.4.1 Antithetic Variables
4.4.2 Control Variates
4.5 Problems
4.6 Notes
4.6.1 Monitoring Importance Sampling Convergence
4.6.2 Accept Reject with Loose Bounds
4.6.3 Partitioning
5 Monte Carlo Optimization
5.1 Introduction
5.2 Stochastic Exploration
5.2.1 A Basic Solution
5.2.2 Gradient Methods
5.2.3. Simulated Annealing
5.2.4 Prior Feedback
5.3 Stochastic Approximation
5.3.1 Missing Data Models and Demarginalization
5.3.2 The EM Algorithm
5.3.3 Monte Carlo EM
5.3.4 EM Standard Errors
……
6 Markov Chains
7 The Metropolis-Hastings Algorithm
8 The Slice Sampler
9 The Two-Stage Gibbs Sampler
10 The Multi-Stage Gibbs Sampler
11 Variable Dimension Models and Reversible Jump Algorithms
12 Diagnosing Convergence
13 Perfect Sampling
14 Iterated and Sequential Importance Sampling
A Probability Distributions
B Notation
References
Index
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