Computational Statistics, 2nd Edition

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