This new edition continues to serve as a comprehensive guide to modern and classical methods of statistical computing. The book is comprised of four main parts spanning the field: Optimization Integration and Simulation Bootstrapping Density Estimation and Smoothing Within these sections,each chapter includes a comprehensive introduction and step-by-step implementation summaries to accompany the explanations of key methods. The new edition includes updated coverage and existing topics as well as new topics such as adaptive MCMC and bootstrapping for correlated data. The book website now includes comprehensive R code for the entire book. There are extensive exercises, real examples, and helpful insights about how to use the methods in practice.

This new edition continues to serve as a comprehensive guide tomodern and classical methods of statistical computing. Thebook is comprised of four main parts spanning the field:* Optimization* Integration and Simulation* Bootstrapping* Density Estimation and SmoothingWithin these sections,each chapter includes a comprehensiveintroduction and step-by-step implementation summaries to accompanythe explanations of key methods. The new edition includesupdated coverage and existing topics as well as new topics such asadaptive MCMC and bootstrapping for correlated data. The bookwebsite now includes comprehensive R code for the entirebook. There are extensive exercises, real examples, andhelpful insights about how to use the methods in practice.

PREFACE xvACKNOWLEDGMENTS xvii1 REVIEW 11.1 Mathematical Notation 11.2 Taylor's Theorem and Mathematical Limit Theory 21.3 Statistical Notation and Probability Distributions 41.4 Likelihood Inference 91.5 Bayesian Inference 111.6 Statistical Limit Theory 131.7 Markov Chains 141.8 Computing 17PART I OPTIMIZATION2 OPTIMIZATION AND SOLVING NONLINEAR EQUATIONS212.1 Univariate Problems 222.2 Multivariate Problems 34Problems 543 COMBINATORIAL OPTIMIZATION 593.1 Hard Problems and NP-Completeness 593.2 Local Search 653.3 Simulated Annealing 683.4 Genetic Algorithms 753.5 Tabu Algorithms 85Problems 924 EM OPTIMIZATION METHODS 974.1 Missing Data, Marginalization, and Notation 974.2 The EM Algorithm 984.3 EM Variants 111Problems 121PART II INTEGRATION AND SIMULATION5 NUMERICAL INTEGRATION 1295.1 Newton-Côtes Quadrature 1295.2 Romberg Integration 1395.3 Gaussian Quadrature 1425.4 Frequently Encountered Problems 146Problems 1486 SIMULATION AND MONTE CARLO INTEGRATION1516.1 Introduction to the Monte Carlo Method 1516.2 Exact Simulation 1526.3 Approximate Simulation 1636.4 Variance Reduction Techniques 180Problems 1957 MARKOV CHAIN MONTE CARLO 2017.1 Metropolis-Hastings Algorithm 2027.2 Gibbs Sampling 2097.3 Implementation 218Problems 2308 ADVANCED TOPICS IN MCMC 2378.1 Adaptive MCMC 2378.2 Reversible Jump MCMC 2508.3 Auxiliary Variable Methods 2568.4 Other Metropolis-Hastings Algorithms 2608.5 Perfect Sampling 2648.6 Markov Chain Maximum Likelihood 2688.7 Example: MCMC for Markov Random Fields 269Problems 279PART III BOOTSTRAPPING9 BOOTSTRAPPING 2879.1 The Bootstrap Principle 2879.2 Basic Methods 2889.3 Bootstrap Inference 2929.4 Reducing Monte Carlo Error 3029.5 Bootstrapping Dependent Data 3039.6 Bootstrap Performance 3159.7 Other Uses of the Bootstrap 3169.8 Permutation Tests 317Problems 319PART IV DENSITY ESTIMATION AND SMOOTHING10 NONPARAMETRIC DENSITY ESTIMATION 32510.1 Measures of Performance 32610.2 Kernel Density Estimation 32710.3 Nonkernel Methods 34110.4 Multivariate Methods 345Problems 35911 BIVARIATE SMOOTHING 36311.1 Predictor-Response Data 36311.2 Linear Smoothers 36511.3 Comparison of Linear Smoothers 37711.4 Nonlinear Smoothers 37911.5 Confidence Bands 38411.6 General Bivariate Data 388Problems 38912 MULTIVARIATE SMOOTHING 39312.1 Predictor-Response Data 39312.2 General Multivariate Data 413Problems 416DATA ACKNOWLEDGMENTS 421REFERENCES 423INDEX 457