Computational Statistics Handbook With Matlab

by Martinez; Wendy L.

• ISBN13: 9781584882299
• ISBN10: 1584882298
• Format: Hardcover
• Copyright: 2001-09-26
• Publisher: Chapman & Hall/

Summary

Focusing on the computational aspects of statistics rather than the theoretical, this handbook uses a down-to-earth approach that makes statistics accessible to a wide range of users. The authors include algorithmic descriptions and MATLAB code for many of the latest methods in computational statistics. Detailed procedures are also included for readers who do not know MATLAB so they can implement the algorithms using other software packages. As a companion to the handbook, MATLAB functions are available for download that implement the techniques described in the text. This is the first book on the market to show how to use MATLAB to execute a wide variety of computational statistics methods and techniques.

Table of Contents

Preface	xv
Introduction
What Is Computational Statistics?	1	(1)
An Overview of the Book	2	(4)
Philosophy	2	(1)
What Is Covered	3	(2)
A Word About Notation	5	(1)
Matlab Code	6	(2)
Computational Statistics Toolbox	7	(1)
Internet Resources	7	(1)
Further Reading	8	(3)
Probability Concepts
Introduction	11	(1)
Probability	12	(5)
Background	12	(2)
Probability	14	(3)
Axioms of Probability	17	(1)
Conditional Probability and Independence	17	(4)
Conditional Probability	17	(1)
Independence	18	(1)
Bayes Theorem	19	(2)
Expectation	21	(3)
Mean and Variance	21	(2)
Skewness	23	(1)
Kurtosis	23	(1)
Common Distributions	24	(21)
Binomial	24	(2)
Poisson	26	(3)
Uniform	29	(2)
Normal	31	(2)
Exponential	33	(3)
Gamma	36	(1)
Chi-Square	37	(1)
Weibull	38	(2)
Beta	40	(1)
Multivariate Normal	41	(4)
Matlab Code	45	(1)
Further Reading	46	(5)
Exercises	48	(3)
Sampling Concepts
Introduction	51	(1)
Sampling Terminology and Concepts	51	(7)
Sample Mean and Sample Variance	53	(1)
Sample Moments	54	(2)
Covariance	56	(2)
Sampling Distributions	58	(2)
Parameter Estimation	60	(8)
Bias	61	(1)
Mean Squared Error	61	(1)
Relative Efficiency	62	(1)
Standard Error	62	(1)
Maximum Likelihood Estimation	63	(3)
Method of Moments	66	(2)
Empirical Distribution Function	68	(5)
Quantiles	69	(4)
Matlab Code	73	(1)
Further Reading	74	(5)
Exercises	76	(3)
Generating Random Variables
Introduction	79	(1)
General Techniques for Generating Random Variables	79	(10)
Uniform Random Numbers	79	(3)
Inverse Transform Method	82	(3)
Acceptance-Rejection Method	85	(4)
Generating Continuous Random Variables	89	(11)
Normal Distribution	89	(1)
Exponential Distribution	89	(2)
Gamma	91	(2)
Chi-Square	93	(2)
Beta	95	(1)
Multivariate Normal	96	(3)
Generating Variates on a Sphere	99	(1)
Generating Discrete Random Variables	100	(6)
Binomial	100	(2)
Poisson	102	(2)
Discrete Uniform	104	(2)
Matlab Code	106	(1)
Further Reading	107	(4)
Exercises	109	(2)
Exploratory Data Analysis
Introduction	111	(1)
Exploring Univariate Data	112	(23)
Histograms	113	(3)
Stem-and-Leaf	116	(3)
Quantile-Based Plots - Continuous Distributions	119	(1)
Q-Q Plot	119	(4)
Quantile Plots	123	(3)
Quantile Plots - Discrete Distributions	126	(1)
Poissonness Plot	126	(3)
Binomialness Plot	129	(3)
Box Plots	132	(3)
Exploring Bivariate and Trivariate Data	135	(12)
Scatterplots	135	(3)
Surface Plots	138	(1)
Contour Plots	138	(3)
Bivariate Histogram	141	(4)
3-D Scatterplot	145	(2)
Exploring Multi-Dimensional Data	147	(36)
Scatterplot Matrix	147	(2)
Slices and Isosurfaces	149	(6)
Star Plots	155	(2)
Andrews Curves	157	(5)
Parallel Coordinates	162	(6)
Projection Pursuit	168	(3)
Projection Pursuit Index	171	(1)
Finding the Structure	172	(2)
Structure Removal	174	(4)
Grand Tour	178	(5)
Matlab Code	183	(1)
Further Reading	184	(7)
Exercises	187	(4)
Monte Carlo Methods for Inferential Statistics
Introduction	191	(1)
Classical Inferential Statistics	192	(12)
Hypothesis Testing	192	(9)
Confidence Intervals	201	(3)
Monte Carlo Methods for Inferential Statistics	204	(10)
Basic Monte Carlo Procedure	204	(1)
Monte Carlo Hypothesis Testing	205	(5)
Monte Carlo Assessment of Hypothesis Testing	210	(4)
Bootstrap Methods	214	(12)
General Bootstrap Methodology	214	(2)
Bootstrap Estimate of Standard Error	216	(3)
Bootstrap Estimate of Bias	219	(1)
Bootstrap Confidence Intervals	220	(1)
Bootstrap Standard Confidence Interval	220	(1)
Bootstrap-t Confidence Interval	221	(3)
Bootstrap Percentile Interval	224	(2)
Matlab Code	226	(1)
Further Reading	227	(4)
Exercises	228	(3)
Data Partitioning
Introduction	231	(1)
Cross-Validation	232	(7)
Jackknife	239	(8)
Better Bootstrap Confidence Intervals	247	(4)
Jackknife-After-Bootstrap	251	(2)
Matlab Code	253	(1)
Further Reading	254	(5)
Exercises	256	(3)
Probability Density Estimation
Introduction	259	(2)
Histograms	261	(19)
1-D Histograms	261	(6)
Multivariate Histograms	267	(2)
Frequency Polygons	269	(5)
Averaged Shifted Histograms	274	(6)
Kernel Density Estimation	280	(7)
Univariate Kernel Estimators	280	(5)
Multivariate Kernel Estimators	285	(2)
Finite Mixtures	287	(19)
Univariate Finite Mixtures	289	(2)
Visualizing Finite Mixtures	291	(2)
Multivariate Finite Mixtures	293	(3)
EM Algorithm for Estimating the Parameters	296	(5)
Adaptive Mixtures	301	(5)
Generating Random Variables	306	(5)
Matlab Code	311	(1)
Further Reading	311	(6)
Exercises	314	(3)
Statistical Pattern Recognition
Introduction	317	(2)
Bayes Decision Theory	319	(13)
Estimating Class-Conditional Probabilities Parametric Method	321	(1)
Estimating Class-Conditional Probabilities: Nonparametric	322	(1)
Bayes Decision Rule	323	(6)
Likelihood Ratio Approach	329	(3)
Evaluating the Classifier	332	(10)
Independent Test Sample	333	(2)
Cross-Validation	335	(2)
Receiver Operating Characteristic (ROC) Curve	337	(5)
Classification Trees	342	(25)
Growing the Tree	347	(5)
Pruning the Tree	352	(4)
Choosing the Best Tree	356	(1)
Selecting the Best Tree Using an Independent Test Sample	357	(4)
Selecting the Best Tree Using Cross-Validation	361	(6)
Clustering	367	(9)
Measures of Distance	367	(2)
Hierarchical Clustering	369	(4)
K-Means Clustering	373	(3)
Matlab Code	376	(3)
Further Reading	379	(6)
Exercises	381	(4)
Nonparametric Regression
Introduction	385	(5)
Smoothing	390	(11)
Loess	391	(5)
Robust Loess Smoothing	396	(4)
Upper and Lower Smooths	400	(1)
Kernel Methods	401	(6)
Nadaraya-Watson Estimator	404	(1)
Local Linear Kernel Estimator	405	(2)
Regression Trees	407	(12)
Growing a Regression Tree	410	(1)
Pruning a Regression Tree	411	(1)
Selecting a Tree	412	(7)
Matlab Code	419	(1)
Further Reading	420	(5)
Exercises	422	(3)
Markov Chain Monte Carlo Methods
Introduction	425	(1)
Background	426	(4)
Bayesian Inference	426	(1)
Monte Carlo Integration	427	(2)
Markov Chains	429	(1)
Analyzing the Output	430	(1)
Metropolis-Hastings Algorithms	430	(13)
Metropolis-Hastings Sampler	431	(2)
Metropolis Sampler	433	(5)
Independence Sampler	438	(1)
Autoregressive Generating Density	439	(4)
The Gibbs Sampler	443	(9)
Convergence Monitoring	452	(6)
Gelman and Rubin Method	453	(5)
Raftery and Lewis Method	458	(1)
Matlab Code	458	(3)
Further Reading	461	(4)
Exercises	462	(3)
Spatial Statistics
Introduction	465	(6)
What Is Spatial Statistics?	465	(1)
Types of Spatial Data	466	(1)
Spatial Point Patterns	467	(2)
Complete Spatial Randomness	469	(2)
Visualizing Spatial Point Processes	471	(4)
Exploring First-order and Second-order Properties	475	(10)
Estimating the Intensity	475	(3)
Estimating the Spatial Dependence	478	(1)
Nearest Neighbor Distances - G and F Distributions	478	(4)
K-Function	482	(3)
Modeling Spatial Point Processes	485	(10)
Nearest Neighbor Distances	486	(4)
K-Function	490	(5)
Simulating Spatial Point Processes	495	(10)
Homogeneous Poisson Process	495	(2)
Binomial Process	497	(2)
Poisson Cluster Process	499	(2)
Inhibition Process	501	(3)
Strauss Process	504	(1)
Matlab Code	505	(2)
Further Reading	507	(4)
Exercises	508	(3)
Appendix A Introduction to Matlab
A.1 What Is Matlab?	511	(1)
A.2 Getting Help in Matlab	512	(1)
A.3 File and Workspace Management	512	(2)
A.4 Punctuation in Matlab	514	(1)
A.5 Arithmetic Operators	514	(2)
A.6 Data Constructs in Matlab	516	(2)
Basic Data Constructs	516	(1)
Building Arrays	516	(1)
Cell Arrays	517	(1)
A.7 Script Files and Functions	518	(2)
A.8 Control Flow	520	(1)
For Loop	520	(1)
While Loop	520	(1)
If-Else Statements	521	(1)
Switch Statement	521	(1)
A.9 Simple Plotting	521	(3)
A.10 Contact Information	524	(1)
Appendix B Index of Notation	525	(22)
Appendix C Projection Pursuit Indexes
C.1 Indexes	529	(3)
Friedman-Tukey Index	529	(1)
Entropy Index	530	(1)
Moment Index	530	(1)
Distances	531	(1)
C.2 Matlab Source Code	532	(7)
Appendix D Matlab Code
D.1 Bootstrap Confidence Interval	539	(1)
D.2 Adaptive Mixtures Density Estimation	540	(2)
D.3 Classification Trees	542	(2)
D.4 Regression Trees	544	(3)
Appendix E Matlab Statistics Toolbox	547	(10)
Appendix F Computational Statistics Toolbox	557	(6)
Appendix G Data Sets	563	(8)
References	571	(14)
Index	585