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Computational Statistics, 2nd Edition

Book Description

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.

    Note: The ebook version does not provide access to the companion files.

    Table of Contents

    1. Cover
    2. Wiley Series in Computational Statistics
    3. Title Page
    4. Copyright
    5. Dedication
    6. Preface
    7. Acknowledgements
    8. Chapter 1: Review
      1. 1.1 Mathematical Notation
      2. 1.2 Taylor's Theorem and Mathematical Limit Theory
      3. 1.3 Statistical Notation and Probability Distributions
      4. 1.4 Likelihood Inference
      5. 1.5 Bayesian Inference
      6. 1.6 Statistical Limit Theory
      7. 1.7 Markov Chains
      8. 1.8 Computing
    9. Part I: Optimization
      1. Chapter 2: Optimization and Solving Nonlinear Equations
        1. 2.1 Univariate Problems
        2. 2.2 Multivariate Problems
      2. Chapter 3: Combinatorial Optimization
        1. 3.1 Hard problems and NP-completeness
        2. 3.2 Local search
        3. 3.3 Simulated Annealing
        4. 3.4 Genetic algorithms
        5. 3.5 Tabu algorithms
      3. Chapter 4: Em Optimization Methods
        1. 4.1 Missing Data, Marginalization, and Notation
        2. 4.2 The EM Algorithm
        3. 4.3 EM Variants
    10. Part II: Integration and Simulation
      1. Chapter 5: Numerical Integration
        1. 5.1 Newton–Côtes Quadrature
        2. 5.2 Romberg Integration
        3. 5.3 Gaussian Quadrature
        4. 5.4 Frequently Encountered Problems
      2. Chapter 6: Simulation and Monte Carlo Integration
        1. 6.1 Introduction to the Monte Carlo Method
        2. 6.2 Exact Simulation
        3. 6.3 Approximate Simulation
        4. 6.4 Variance Reduction Techniques
      3. Chapter 7: Markov Chain Monte Carlo
        1. 7.1 Metropolis–Hastings algorithm
        2. 7.2 Gibbs Sampling
        3. 7.3 Implementation
      4. Chapter 8: Advanced Topics in MCMC
        1. 8.1 Adaptive MCMC
        2. 8.2 Reversible Jump MCMC
        3. 8.3 Auxiliary variable methods
        4. 8.4 Other Metropolis–Hastings Algorithms
        5. 8.5 Perfect sampling
        6. 8.6 Markov Chain Maximum Likelihood
        7. 8.7 Example: MCMC for Markov random fields
    11. Part III: Bootstrapping
      1. Chapter 9: Bootstrapping
        1. 9.1 The Bootstrap Principle
        2. 9.2 Basic methods
        3. 9.3 Bootstrap Inference
        4. 9.4 Reducing Monte Carlo error
        5. 9.5 Bootstrapping dependent data
        6. 9.6 Bootstrap Performance
        7. 9.7 Other uses of the bootstrap
        8. 9.8 Permutation Tests
    12. Part IV: Density Estimation and Smoothing
      1. Chapter 10: Nonparametric Density Estimation
        1. 10.1 Measures of Performance
        2. 10.2 Kernel Density Estimation
        3. 10.3 Nonkernel Methods
        4. 10.4 Multivariate Methods
      2. Chapter 11: Bivariate Smoothing
        1. 11.1 Predictor–Response Data
        2. 11.2 Linear Smoothers
        3. 11.3 Comparison of Linear Smoothers
        4. 11.4 Nonlinear Smoothers
        5. 11.5 Confidence Bands
        6. 11.6 General Bivariate Data
      3. Chapter 12: Multivariate Smoothing
        1. 12.1 Predictor–Response Data
        2. 12.2 General Multivariate Data
    13. Data Acknowledgments
    14. References
    15. Index
    16. Wiley Series in Computational Statistics