COMPUTATIONAL STATISTICS; CONTENTS; PREFACE; ACKNOWLEDGMENTS; 1 REVIEW; 1.1 Mathematical Notation; 1.2 Taylor's Theorem and Mathematical Limit Theory; 1.3 Statistical Notation and Probability Distributions; 1.4 Likelihood Inference; 1.5 Bayesian Inference; 1.6 Statistical Limit Theory; 1.7 Markov Chains; 1.8 Computing; PART I: OPTIMIZATION; 2 OPTIMIZATION AND SOLVING NONLINEAR EQUATIONS; 2.1 Univariate Problems; 2.1.1 Newton's Method; 2.1.1.1 Convergence Order; 2.1.2 Fisher Scoring; 2.1.3 Secant Method; 2.1.4 Fixed-Point Iteration; 2.1.4.1 Scaling; 2.2 Multivariate Problems.

2.2.1 Newton's Method and Fisher Scoring; 2.2.1.1 Iteratively Reweighted Least Squares; 2.2.2 Newton-Like Methods; 2.2.2.1 Ascent Algorithms; 2.2.2.2 Discrete Newton and Fixed-Point Methods; 2.2.2.3 Quasi-Newton Methods; 2.2.3 Gauss-Newton Method; 2.2.4 Nelder-Mead Algorithm; 2.2.5 Nonlinear Gauss-Seidel Iteration; Problems; 3 COMBINATORIAL OPTIMIZATION; 3.1 Hard Problems and NP-Completeness; 3.1.1 Examples; 3.1.2 Need for Heuristics; 3.2 Local Search; 3.3 Simulated Annealing; 3.3.1 Practical Issues; 3.3.1.1 Neighborhoods and Proposals; 3.3.1.2 Cooling Schedule and Convergence.

3.3.2 Enhancements; 3.4 Genetic Algorithms; 3.4.1 Definitions and the Canonical Algorithm; 3.4.1.1 Basic Definitions; 3.4.1.2 Selection Mechanisms and Genetic Operators; 3.4.1.3 Allele Alphabets and Genotypic Representation; 3.4.1.4 Initialization, Termination, and Parameter Values; 3.4.2 Variations; 3.4.2.1 Fitness; 3.4.2.2 Selection Mechanisms and Updating Generations; 3.4.2.3 Genetic Operators and Permutation Chromosomes; 3.4.3 Initialization and Parameter Values; 3.4.4 Convergence; 3.5 Tabu Algorithms; 3.5.1 Basic Definitions; 3.5.2 The Tabu List; 3.5.3 Aspiration Criteria.

3.5.4 Diversification; 3.5.5 Intensification; 3.5.6 Comprehensive Tabu Algorithm; Problems; 4 EM OPTIMIZATION METHODS; 4.1 Missing Data, Marginalization, and Notation; 4.2 The EM Algorithm; 4.2.1 Convergence; 4.2.2 Usage in Exponential Families; 4.2.3 Variance Estimation; 4.2.3.1 Louis's Method; 4.2.3.2 SEM Algorithm; 4.2.3.3 Bootstrapping; 4.2.3.4 Empirical Information; 4.2.3.5 Numerical Differentiation; 4.3 EM Variants; 4.3.1 Improving the E Step; 4.3.1.1 Monte Carlo EM; 4.3.2 Improving the M Step; 4.3.2.1 ECM Algorithm; 4.3.2.2 EM Gradient Algorithm; 4.3.3 Acceleration Methods.

4.3.3.1 Aitken Acceleration; 4.3.3.2 Quasi-Newton Acceleration; Problems; PART II: INTEGRATION AND SIMULATION; 5 NUMERICAL INTEGRATION; 5.1 Newton-Côtes Quadrature; 5.1.1 Riemann Rule; 5.1.2 Trapezoidal Rule; 5.1.3 Simpson's Rule; 5.1.4 General kth-Degree Rule; 5.2 Romberg Integration; 5.3 Gaussian Quadrature; 5.3.1 Orthogonal Polynomials; 5.3.2 The Gaussian Quadrature Rule; 5.4 Frequently Encountered Problems; 5.4.1 Range of Integration; 5.4.2 Integrands with Singularities or Other Extreme Behavior; 5.4.3 Multiple Integrals; 5.4.4 Adaptive Quadrature; 5.4.5 Software for Exact Integration Problems.

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.

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