## Table of contents for Computational statistics handbook with MATLAB / Wendy L. Martinez and Angel R. Martinez.

Bibliographic record and links to related information available from the Library of Congress catalog.

Note: Contents data are machine generated based on pre-publication provided by the publisher. Contents may have variations from the printed book or be incomplete or contain other coding.

```
Preface to the Second Edition.......................................................................... xvii
Preface to the First Edition .................................................................................xxi
Chapter 1
Introduction
1.1 What Is Computational Statistics? .................................................................1
1.2 An Overview of the Book ...............................................................................2
Philosophy..................................................................................................... 2
What Is Covered ........................................................................................... 3
1.3 Matlab Code ......................................................................................................6
Computational Statistics Toolbox .............................................................. 7
Internet Resources ........................................................................................ 8
Chapter 2
Probability Concepts
2.1 Introduction ....................................................................................................11
2.2 Probability .......................................................................................................12
Background ................................................................................................. 12
Probability ................................................................................................... 14
Axioms of Probability ................................................................................ 17
2.3 Conditional Probability and Independence ...............................................17
Conditional Probability ............................................................................. 17
Independence.............................................................................................. 18
Bayes Theorem............................................................................................ 19
2.4 Expectation ......................................................................................................21
Mean and Variance .................................................................................... 21
Skewness...................................................................................................... 23
Kurtosis ........................................................................................................ 23
2.5 Common Distributions ..................................................................................24
Binomial....................................................................................................... 24
Poisson ......................................................................................................... 26
Uniform........................................................................................................ 29
Normal ......................................................................................................... 31
Exponential.................................................................................................. 33
Gamma......................................................................................................... 36
Chi-Square................................................................................................... 37
Weibull......................................................................................................... 38
Beta ............................................................................................................... 40
Student¿s t Distribution ............................................................................. 41
Multivariate Normal .................................................................................. 44
Multivariate t Distribution ........................................................................ 47
2.6 Matlab Code ....................................................................................................48
Exercises ................................................................................................................51
Chapter 3
Sampling Concepts
3.1 Introduction ....................................................................................................55
3.2 Sampling Terminology and Concepts ........................................................55
Sample Mean and Sample Variance ........................................................ 57
Sample Moments........................................................................................ 58
Covariance................................................................................................... 60
3.3 Sampling Distributions .................................................................................63
3.4 Parameter Estimation ....................................................................................64
Bias................................................................................................................ 66
Mean Squared Error................................................................................... 66
Relative Efficiency ...................................................................................... 67
Standard Error ............................................................................................ 67
Maximum Likelihood Estimation ............................................................ 68
Method of Moments................................................................................... 71
3.5 Empirical Distribution Function ..................................................................72
Quantiles...................................................................................................... 74
3.6 Matlab Code ....................................................................................................77
Exercises ................................................................................................................80
Chapter 4
Generating Random Variables
4.1 Introduction ....................................................................................................83
4.2 General Techniques for Generating Random Variables ...........................83
Uniform Random Numbers...................................................................... 83
Inverse Transform Method ....................................................................... 86
Acceptance-Rejection Method .................................................................. 89
4.3 Generating Continuous Random Variables ...............................................93
Normal Distribution .................................................................................. 93
Exponential Distribution ........................................................................... 93
Gamma......................................................................................................... 95
Chi-Square................................................................................................... 97
Beta ............................................................................................................... 99
Multivariate Normal ................................................................................ 100
Multivariate Student¿s t Distribution .................................................... 103
Generating Variates on a Sphere............................................................ 104
4.4 Generating Discrete Random Variables ...................................................107
Binomial..................................................................................................... 107
Poisson ....................................................................................................... 108
Discrete Uniform...................................................................................... 111
4.5 Matlab Code ..................................................................................................112
Exercises ..............................................................................................................115
Chapter 5
Exploratory Data Analysis
5.1 Introduction ..................................................................................................117
5.2 Exploring Univariate Data ..........................................................................119
Histograms ................................................................................................ 119
Stem-and-Leaf........................................................................................... 122
Quantile-Based Plots - Continuous Distributions ............................... 124
Quantile Plots - Discrete Distributions.................................................. 132
Box Plots .................................................................................................... 139
5.3 Exploring Bivariate and Trivariate Data ...................................................145
Scatterplots ................................................................................................ 145
Surface Plots .............................................................................................. 147
Contour Plots ............................................................................................ 148
Bivariate Histogram................................................................................. 149
3-D Scatterplot .......................................................................................... 156
5.4 Exploring Multi-Dimensional Data ...........................................................157
Scatterplot Matrix ..................................................................................... 158
Slices and Isosurfaces............................................................................... 159
Glyphs........................................................................................................ 165
Andrews Curves....................................................................................... 169
Parallel Coordinates................................................................................. 173
5.5 Matlab Code ..................................................................................................179
Exercises ..............................................................................................................183
Chapter 6
Finding Structure
6.1 Introduction ..................................................................................................187
6.2 Principal Component Analysis ..................................................................189
6.3 Projection Pursuit EDA ...............................................................................194
Projection Pursuit Index .......................................................................... 197
Finding the Structure ............................................................................... 198
Structure Removal.................................................................................... 199
6.4 Independent Component Analysis ...........................................................205
6.5 Grand Tour ...................................................................................................210
6.6 Nonlinear Dimensionality Reduction .......................................................214
Multidimensional Scaling ....................................................................... 215
Isometric Feature Mapping - ISOMAP ................................................. 218
6.7 Matlab Code ..................................................................................................224
Exercises ..............................................................................................................227
Chapter 7
Monte Carlo Methods for Inferential Statistics
7.1 Introduction ..................................................................................................229
7.2 Classical Inferential Statistics .....................................................................230
Hypothesis Testing................................................................................... 230
Confidence Intervals ................................................................................ 239
7.3 Monte Carlo Methods for Inferential Statistics ........................................242
Basic Monte Carlo Procedure ................................................................. 242
Monte Carlo Hypothesis Testing ........................................................... 243
Monte Carlo Assessment of Hypothesis Testing................................. 248
7.4 Bootstrap Methods .......................................................................................252
General Bootstrap Methodology............................................................ 252
Bootstrap Estimate of Standard Error ................................................... 254
Bootstrap Estimate of Bias....................................................................... 257
Bootstrap Confidence Intervals .............................................................. 258
7.5 Matlab Code ..................................................................................................264
Exercises ..............................................................................................................266
Chapter 8
Data Partitioning
8.1 Introduction ..................................................................................................269
8.2 Cross-Validation ...........................................................................................270
8.3 Jackknife ........................................................................................................277
8.4 Better Bootstrap Confidence Intervals ......................................................285
8.5 Jackknife-After-Bootstrap ...........................................................................289
8.6 Matlab Code ..................................................................................................291
Exercises ..............................................................................................................294
Chapter 9
Probability Density Estimation
9.1 Introduction ..................................................................................................297
9.2 Histograms ....................................................................................................299
1-D Histograms......................................................................................... 299
Multivariate Histograms ......................................................................... 305
Frequency Polygons................................................................................. 307
Averaged Shifted Histograms ................................................................ 312
9.3 Kernel Density Estimation ..........................................................................318
Univariate Kernel Estimators ................................................................. 318
Multivariate Kernel Estimators .............................................................. 323
9.4 Finite Mixtures .............................................................................................325
Univariate Finite Mixtures ...................................................................... 327
Visualizing Finite Mixtures..................................................................... 329
Multivariate Finite Mixtures................................................................... 331
EM Algorithm for Estimating the Parameters ..................................... 334
9.5 Generating Random Variables ...................................................................344
9.6 Matlab Code ..................................................................................................348
Exercises ..............................................................................................................351
Chapter 10
Supervised Learning
10.1 Introduction ................................................................................................355
10.2 Bayes Decision Theory ..............................................................................357
Estimating Class-Conditional Probabilities: Parametric Method ..... 359
Estimating Class-Conditional Probabilities: Nonparametric............. 360
Bayes Decision Rule ................................................................................. 362
Likelihood Ratio Approach..................................................................... 368
10.3 Evaluating the Classifier ...........................................................................371
Independent Test Sample........................................................................ 371
Cross-Validation....................................................................................... 373
Receiver Operating Characteristic (ROC) Curve................................. 376
10.4 Classification Trees ....................................................................................382
Growing the Tree...................................................................................... 386
Pruning the Tree ....................................................................................... 390
Choosing the Best Tree ............................................................................ 394
10.5 Combining Classifiers ...............................................................................406
Bagging ...................................................................................................... 406
Boosting ..................................................................................................... 408
Arcing Classifiers ..................................................................................... 410
Random Forests ........................................................................................ 411
10.6 MATLAB Code ...........................................................................................412
Exercises ..............................................................................................................416
Chapter 11
Unsupervised Learning
11.1 Introduction ................................................................................................419
11.2 Measures of Distance .................................................................................420
11.3 Hierarchical Clustering .............................................................................422
1 1.4 K-Means Clustering ..................................................................................429
11.5 Model-Based Clustering ............................................................................433
Finite Mixture Models and the EM Algorithm .................................... 434
Model-Based Agglomerative Clustering .............................................. 438
Bayesian Information Criterion.............................................................. 439
Model-Based Clustering Procedure....................................................... 441
11.6 Assessing Cluster Results .........................................................................445
Mojena ¿ Upper Tail Rule ....................................................................... 445
Silhouette Statistic .................................................................................... 447
Other Methods for Evaluating Clusters................................................ 449
11.6 Matlab Code ................................................................................................452
Exercises ..............................................................................................................455
Chapter 12
Parametric Models
12.1 Introduction ................................................................................................457
12.2 Spline Regression Models .........................................................................461
12.3 Logistic Regression ....................................................................................467
Creating the Model .................................................................................. 468
Interpreting the Model Parameters........................................................ 471
12.4 Generalized Linear Models ......................................................................474
Exponential Form ..................................................................................... 474
Generalized Linear Model ...................................................................... 480
Model Checking........................................................................................ 485
12.5 MATLAB Code ...........................................................................................493
Exercises ..............................................................................................................496
Chapter 13
Nonparametric Regression
13.1 Introduction ................................................................................................499
13.2 Some Smoothing Methods ........................................................................500
Bin Smoothing........................................................................................... 501
Running Mean .......................................................................................... 503
Running Line............................................................................................. 504
Local Polynomial Regression - Loess .................................................... 505
Robust Loess ............................................................................................. 510
13.3 Kernel Methods ..........................................................................................514
Local Linear Kernel Estimator................................................................ 518
13.4 Smoothing Splines .....................................................................................521
Natural Cubic Splines.............................................................................. 521
Reinsch Method for Finding Smoothing Splines................................. 523
Values for a Cubic Smoothing Spline.................................................... 525
Weighted Smoothing Spline ................................................................... 526
13.5 Nonparametric Regression - Other Details ............................................528
Choosing the Smoothing Parameter...................................................... 528
Estimation of the Residual Variance...................................................... 533
Variability of Smooths ............................................................................. 533
13.6 Regression Trees .........................................................................................537
Growing a Regression Tree..................................................................... 539
Pruning a Regression Tree ...................................................................... 541
Selecting a Tree ......................................................................................... 543
13.8 Matlab Code ................................................................................................553
Exercises ..............................................................................................................559
Chapter 14
Markov Chain Monte Carlo Methods
14.1 Introduction ................................................................................................561
14.2 Background .................................................................................................562
Bayesian Inference.................................................................................... 562
Monte Carlo Integration.......................................................................... 563
Markov Chains ......................................................................................... 565
Analyzing the Output.............................................................................. 566
14.3 Metropolis-Hastings Algorithms .............................................................566
Metropolis-Hastings Sampler................................................................. 567
Metropolis Sampler.................................................................................. 569
Independence Sampler ............................................................................ 574
Autoregressive Generating Density ...................................................... 575
14.4 The Gibbs Sampler .....................................................................................579
14.5 Convergence Monitoring ..........................................................................588
Gelman and Rubin Method .................................................................... 589
Raftery and Lewis Method...................................................................... 594
14.6 Matlab Code ................................................................................................594
Exercises ..............................................................................................................598
Chapter 15
Spatial Statistics
15.1 Introduction ................................................................................................603
What Is Spatial Statistics?........................................................................ 603
Types of Spatial Data ............................................................................... 604
Spatial Point Patterns............................................................................... 605
Complete Spatial Randomness............................................................... 607
15.2 Visualizing Spatial Point Processes .........................................................609
15.3 Exploring First-order and Second-order Properties .............................613
Estimating the Intensity........................................................................... 613
Estimating the Spatial Dependence ....................................................... 616
15.4 Modeling Spatial Point Processes ............................................................623
Nearest Neighbor Distances ................................................................... 624
K-Function................................................................................................. 628
15.5 Simulating Spatial Point Processes ..........................................................633
Homogeneous Poisson Process .............................................................. 633
Binomial Process....................................................................................... 635
Poisson Cluster Process ........................................................................... 637
Inhibition Process ..................................................................................... 639
Strauss Process.......................................................................................... 642
15.6 Matlab Code ................................................................................................643
Exercises ..............................................................................................................646
Appendix A
Introduction to Matlab
A.1 What Is Matlab? ..........................................................................................649
A.2 Getting Help in Matlab ..............................................................................650
A.3 File and Workspace Management ............................................................650
A.4 Punctuation in Matlab ................................................................................652
A.5 Arithmetic Operators .................................................................................652
A.6 Data Constructs in Matlab .........................................................................654
Basic Data Constructs .............................................................................. 654
Building Arrays ........................................................................................ 654
Cell Arrays................................................................................................. 655
A.7 Script Files and Functions ..........................................................................656
A.8 Control Flow ................................................................................................658
For Loop..................................................................................................... 658
While Loop ................................................................................................ 658
If-Else Statements ..................................................................................... 659
Switch Statement ...................................................................................... 659
A.9 Simple Plotting ............................................................................................659
A.10 Contact Information .................................................................................662
Appendix B
Projection Pursuit Indexes
B.1 Indexes ..........................................................................................................663
Friedman-Tukey Index ............................................................................ 663
Entropy Index ........................................................................................... 664
Moment Index........................................................................................... 664
Distances.................................................................................................... 665
B.2 Matlab Source Code ....................................................................................666
Appendix C
Matlab Statistics Toolbox
Appendix D
Computational Statistics Toolbox
Appendix E
Exploratory Data Analysis Toolboxes
E.1 Introduction ..................................................................................................689
E.2 Exploratory Data Analysis Toolbox ..........................................................690
E.3 EDA GUI Toolbox .......................................................................................691
Appendix F
Data Sets
References ........................................................................................................... 713
```

Library of Congress Subject Headings for this publication:

Mathematical statistics -- Data processing.
MATLAB.