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