Computational statistics

Title:

Personal Author:

Givens, Geof H.

Series:

Wiley series in computational statistics

Edition:

2nd ed.

Publication Information:

Hoboken, NJ. : Wiley, c2013.

Physical Description:

xviii, 469 p. : ill. ; 25 cm.

ISBN:

9780470533314

Subject Term:

Mathematical statistics -- Data processing

Added Author:

Hoeting, Jennnifer A. (Jennifer Ann), 1966-

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010307164	QA276.4 G58 2013	Open Access Book	Book	Searching... Unknown

Summary

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.

Author Notes

GEOF H. GIVENS, PhD, is Associate Professor in the Department of Statistics at Colorado State University. He serves as Associate Editor for Computational Statistics and Data Analysis. His research interests include statistical problems in wildlife conservation biology including ecology, population modeling and management, and automated computer face recognition.

JENNIFER A. HOETING, PhD, is Professor in the Department of Statistics at Colorado State University. She is an award-winning teacher who co-leads large research efforts for the National Science Foundation. She has served as associate editor for the Journal of the American Statistical Association and Environmetrics. Her research interests include spatial statistics, Bayesian methods, and model selection.

Givens and Hoeting have taught graduate courses on computational statistics for nearly twenty years, and short courses to leading statisticians and scientists around the world.

Preface	p. xv
Acknowledgments	p. xix
1 Review	p. 1
1.1 Mathematical notation	p. 1
1.2 Taylor's theorem and mathematical limit theory	p. 2
1.3 Statistical notation and probability distributions	p. 4
1.4 Likelihood inference	p. 6
1.5 Bayesian inference	p. 11
1.6 Statistical limit theory	p. 13
1.7 Markov chains	p. 14
1.8 Computing	p. 17
Part I Optimization
2 Optimization and Solving Nonlinear Equations	p. 3
2.1 Univariate problems	p. 5
2.2 Multivariate problems	p. 17
Problems	p. 36
3 Combinatorial Optimization	p. 43
3.1 Hard problems and NP-completeness	p. 44
3.2 Local search	p. 50
3.3 Simulated annealing	p. 53
3.4 Genetic algorithms	p. 60
3.5 Tabu algorithms	p. 71
Problems	p. 78
4 EM Optimization Methods	p. 83
4.1 Missing data, marginalization, and notation	p. 84
4.2 The EM algorithm	p. 84
4.3 EM Variants	p. 98
Problems	p. 108
Part II Integration and Simulation
5 Numerical Integration	p. 117
5.1 Newton-Côtes quadrature	p. 118
5.2 Romberg integration	p. 127
5.3 Gaussian quadrature	p. 131
5.4 Frequently encountered problems	p. 135
Problems	p. 137
6 Simulation and Monte Carlo Integration	p. 139
6.1 Introduction to the Monte Carlo method	p. 140
6.3 Approximate Simulation	p. 152
6.4 Variance reduction techniques	p. 170
Problems	p. 185
7 Markov Chain Monte Carlo	p. 191
7.1 Metropolis-Hastings algorithm	p. 192
7.2 Gibbs sampling	p. 199
7.3 Implementation	p. 210
Problems	p. 222
8 Advanced Topics in MCMC	p. 229
8.1 Adaptive MCMC	p. 229
8.2 Reversible Jump MCMC	p. 243
8.3 Auxiliary variable methods	p. 250
8.4 Other Metropolis Hastings Algorithms	p. 254
8.5 Perfect sampling	p. 258
8.6 Markov chain maximum likelihood	p. 262
8.7 Example: MCMC for Markov random fields	p. 263
Problems	p. 274
Part III Approximating Distributions
9 Bootstrapping	p. 281
9.1 The bootstrap principle	p. 281
9.2 Basic methods	p. 283
9.3 Bootstrap inference	p. 286
9.4 Reducing Monte Carlo error	p. 297
9.5 Bootstrapping dependent data	p. 298
9.6 Bootstrap performance	p. 310
9.7 Other uses of the bootstrap	p. 312
9.8 Permutation tests	p. 313
Problems	p. 314
Part IV Density Estimation And Smoothing
10 Nonparametric Density Estimation	p. 321
10.1 Measures of performance	p. 322
10.2 Kernel density estimation	p. 324
10.3 Nonkernel methods	p. 338
10.4 Multivariate methods	p. 341
Problems	p. 356
11 Bivariate Smoothing	p. 361
11.1 Predictor-response data	p. 362
11.2 Linear smoothers	p. 364
11.3 Comparison of linear smoothers	p. 376
11.4 Nonlinear smoothers	p. 378
11.5 Confidence bands	p. 385
11.6 General bivariate data	p. 388
Problems	p. 389
12 Multivariate Smoothing	p. 393
12.1 Predictor-response data	p. 393
12.2 General multivariate data	p. 415
Problems	p. 419
Data Acknowledgments	p. 423
References	p. 425
Index	p. 453

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Summary

Summary

Author Notes

Table of Contents