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Contents
Contents
List of Contributors
I. Computational Statistics
1. Computational Statistics: An Introduction
1.1 Computational Statistics and Data Analysis
1.2 The Emergence of a Field of Computational Statistics
1.3 Why This Handbook
References
II. Statistical Computing
1. Basic Computational Algorithms
1.1 Computer Arithmetic
1.2 Algorithms
References
2. Random Number Generation
2.1 Introduction
2.2 Uniform Random Number Generators
2.3 Linear Recurrences Modulo
2.4 Generators Based on Recurrences Modulo
2.5 Nonlinear RNGs
2.6 Examples of Statistical Tests
2.7 Available Software and Recommendations
2.8 Non-uniform Random Variate Generation
References
3. Markov Chain
Monte Carlo Technology
3.1 Introduction
3.2 Markov Chains
3.3 Metropolis-Hastings Algorithm
3.4 The Gibbs Sampling Algorithm
3.5 MCMC Sampling with Latent Variables
3.6 Estimation of Density Ordinates
3.7 Sampler Performance and Diagnostics
3.8 Strategies for Improving Mixing
3.9 Concluding Remarks
References
4. Numerical Linear Algebra
4.1 Matrix Decompositions
4.2 Direct Methods for Solving Linear Systems
4.3 Iterative Methods for Solving Linear Systems
4.4 Eigenvalues and Eigenvectors
4.5 Sparse Matrices
References
5. The EM Algorithm
5.1 Introduction
5.2 Basic Theory of the EM Algorithm
5.3 Examples of the EM Algorithm
5.4 Variations on the EM Algorithm
5.5 Miscellaneous Topics on the EM Algorithm
References
6. Stochastic Optimization
6.1 Introduction
6.2 Random Search
6.3 Stochastic Approximation
6.4 Genetic Algorithms
6.5 Concluding Remarks
References
7. Transforms in Statistics
7.1 Introduction
7.2 Fourier and Related Transforms
7.3 Wavelets and Other Multiscale Transforms
7.4 Discrete Wavelet Transforms
7.5 Conclusion
References
8. Parallel Computing Techniques
8.1 Introduction
8.2 Basic Ideas
8.3 Parallel Computing Software
8.4 Parallel Computing in Statistics
References
9. Statistical Databases
9.1 Introduction
9.2 Fundamentals of Data Management
9.3 Architectures, Concepts and Operators
9.4 Access Methods
9.5 Extraction, Transformation and Loading (ETL)
9.6 Metadata and XML
9.7 Privacy and Security
References
10. Interactive and Dynamic Graphics
10.1 Introduction
10.2 Early Developments and Software
10.3 Concepts of Interactive and Dynamic Graphics
10.4 Graphical Software
10.5 Interactive 3D Graphics
10.6 Applications in Geography, Medicine, and Environmental Sciences
10.7 Outlook
References
11. The Grammar of Graphics
11.1 Introduction
11.2 Variables
11.3 Algebra
11.4 Scales
11.5 Statistics
11.6 Geometry
11.7 Coordinates
11.8 Aesthetics
11.9 Layout
11.10 Analytics
11.11 Software
11.12 Conclusion
References
12. Statistical User Interfaces
12.1 Introduction
12.2 The Golden Rules and the ISO Norm 9241
12.3 Development of Statistical User Interfaces
12.4 Outlook
Web References
References
13. Object Oriented Computing
13.1 Introduction
13.2 Objects and Encapsulation
13.3 Short Introduction to the UML
13.4 Inheritance
13.5 Polymorphism
13.6 More about Inheritance
13.7 Structure of the Object Oriented Program
13.8 Conclusion
References
III. Statistical Methodology
1. Model Selection
1.1 Introduction
1.2 Basic Concepts - Trade-Offs
1.3 AIC, BIC, C
and Their Variations
1.4 Cross-Validation and Generalized Cross-Validation
1.5 Bayes Factor
1.6 Impact of Heteroscedasticity and Correlation
1.7 Discussion
References
2. Bootstrap and Resampling
2.1 Introduction
2.2 Bootstrap as a Data Analytical Tool
2.3 Resampling Tests and Confidence Intervals
2.4 Bootstrap for Dependent Data
References
3. Design and Analysis of Monte Carlo Experiments
3.1 Introduction
3.2 Simulation Techniques in Computational Statistics
3.3 Black-Box Metamodels of Simulation Models
3.4 Designs for Linear Regression Models
3.5 Kriging
3.6 Conclusions
References
4. Multivariate Density Estimation and Visualization
4.1 Introduction
4.2 Visualization
4.3 Density Estimation Algorithms and Theory
4.4 Visualization of Trivariate Functionals
4.5 Conclusions
References
5. Smoothing: Local Regression Techniques
5.1 Smoothing
5.2 Linear Smoothing
5.3 Statistical Properties of Linear Smoothers
5.4 Statistics for Linear Smoothers: Bandwidth Selection and Inference
5.5 Multivariate Smoothers
References
6. Dimension Reduction Methods
6.1 Introduction
6.2 Linear Reduction of High-dimensional Data
6.3 Nonlinear Reduction of High-dimensional Data
6.4 Linear Reduction of Explanatory Variables
6.5 Concluding Remarks
References
7. Generalized Linear Models
7.1 Introduction
7.2 Model Characteristics
7.3 Estimation
7.4 Practical Aspects
7.5 Complements and Extensions
References
8. (Non) Linear Regression Modeling
8.1 Linear Regression Modeling
8.2 Nonlinear Regression Modeling
References
9. Robust Statistics
9.1 Robust Statistics; Examples and Introduction
9.2 Location and Scale in
9.3 Location and Scale in
9.4 Linear Regression
9.5 Analysis of Variance
References
10. Semiparametric Models
10.1 Introduction
10.2 Semiparametric Models for Conditional Mean Functions
10.3 The Proportional Hazards Model with Unobserved Heterogeneity
10.4 A Binary Response Model
References
11. Bayesian Computational Methods
11.1 Introduction
11.2 Bayesian Computational Challenges
11.3 Monte Carlo Methods
11.4 Markov Chain Monte Carlo Methods
11.5 More Monte Carlo Methods
11.6 Conclusion
References
12. Computational Methods in Survival Analysis
12.1 Introduction
12.2 Estimation of Shape or Power Parameter
12.3 Regression Models
12.4 Multiple Failures and Counting Processes
References
13. Data and Knowledge Mining
13.1 Data Dredging and Knowledge Discovery
13.2 Knowledge Discovery in Databases
13.3 Supervised and Unsupervised Learning
13.4 Data Mining Tasks
13.5 Data Mining Computational Methods
References
14. Recursive Partitioning and Tree-based Methods
14.1 Introduction
14.2 Basic Classification Trees
14.3 Computational Issues
14.4 Interpretation
14.5 Survival Trees
14.6 Tree-based Methods for Multiple Correlated Outcomes
14.7 Remarks
References
15. Support Vector Machines
15.1 Introduction
15.2 Learning from Examples
15.3 Linear SVM: Learning Theory in Practice
15.4 Non-linear SVM
15.5 Implementation of SVM
15.6 Extensions of SVM
15.7 Applications
15.8 Summary and Outlook
References
16. Bagging, Boosting and Ensemble Methods
16.1 An Introduction to Ensemble Methods
16.2 Bagging and Related Methods
16.3 Boosting
References
IV. Selected Applications
1. Computationally Intensive Value at Risk Calculations
1.1 Introduction
1.2 Stable Distributions
1.3 Hyperbolic Distributions
1.4 Value at Risk, Portfolios and Heavy Tails
References
2. Econometrics
2.1 Introduction
2.2 Limited Dependent Variable Models
2.3 Stochastic Volatility and Duration Models
2.4 Finite Mixture Models
References
3. Statistical and Computational Geometry of Biomolecular Structure
3.1 Introduction
3.2 Statistical Geometry of Molecular Systems
3.3 Tetrahedrality of Delaunay Simplices as a Structural Descriptor in Water
3.4 Spatial and Compositional Three-dimensional Patterns in Proteins
3.5 Protein Structure Comparison and Classification
3.6 Conclusions
References
4. Functional Magnetic Resonance Imaging
4.1 Introduction: Overview and Purpose of fMRI
4.2 Background
4.3 fMRI Data
4.4 Modeling and Analysis
4.5 Computational Issues
4.6 Conclusions
References
5. Network Intrusion Detection
5.1 Introduction
5.2 Basic TCP/IP
5.3 Passive Sensing of Denial of Service Attacks
5.4 Streaming Data
5.5 Visualization
5.6 Profiling and Anomaly Detection
5.7 Discussion
References
Index
and Their Variations
