CONTENTS
Preflace xv
Acknowledgments xix
Author xii
PART I Introduction to Probability, Statistics, Time Series, and Spatial Analysis
Chapter 1 Introduction 3
Brief History of Statistical and Probabilistic Analysis 3
Computers 4
Applications 4
Types of Variables 4
Discrete 5
Continuous 5
Discretization 5
Independent vs. Dependent Variables 6
Probability Theory and Random Variables 6
Methodology 6
Descriplive Statistics 7
Inferential Statistics 7
Predictors, Models, and Regression 7
Time Series 8
Spatial Data Analysi 8
Matrices and Multiple Dimensions 8
Other Approaches: Process-Based Models 9
Baby Steps: Calculations and Graphs 9
Mean, Variance, and Standard Deviation of a Sample 9
Simple Graphs as Text: Stem-and-Leaf Plots 10
Histograms 11
Exercises 11
Computer Session: Introduction to R 11
Working Directory 11
Installing R 11
Personalize the R GUI Shortcut 11
Running R 13
Basic R Skills 13
R Console 15
Scripts 15
Graphics Device 16
Downloading Data Files 17
Read a Simple Text Data File 17
Simple Statistics 19
Simple Graphs as Text: Stem-and-Leaf Plots 20
Simple Graphs to a Graphics Window 20
Addressing Entries of an Array 20
Example: Salinity 22
CSV Text Files 23
Store Your Data Files and Objects 24
Command History and Long Sequences of Commands 25
Editing Data in Objects 25
Cleanup and Close R .Session 26
Computer Exercises 26
Supplementary Reading 27
Chapter 2 Probability Theory 29
Events and Probabilities 29
Algebra of Events 29
Combinations 31
Probability Trees 32
Conditional Probability 33
Testing Water Quality: False Negative and False Positive 34
Bayes' Theorem 35
Generalization of Bayes' Rule to Many Events 36
Bio-Sensing 36
Decision Making 37
Exercises 39
Computer Session: Introduction to Rcmdr, Programming,
and Multiple Plots 40
R Commander 40
Package Installation and Loading 40
R GUI SDI Option: Best for R Commander 43
How to Import a Text Data File Using Rcmdr 43
Simple Graphs on a Text Window 45
Simple Graphs on a Graphics Window: Histograms 46
More than One Variable: Reading Files and Plot Variables 47
Using the R Console 48
Using the R Commander 51
Programming Loops 53
Application: Bayes' Theorem 54
Application: Decision Making 55
More on Graphics Windows 55
Editing Data in Objects 56
Clean Up and Exit 56
Additional GUIs to Use R 57
Modifying the R Commander 57
Other Packages to Be Used in the Book 57
Computer Exercises 58
Supplementary Reading 58
Chapter 3 Random Variables, Distributions, Moments, and Statistics 59
Random Variables 59
Distributions 59
Contents vii
Probability Mass and Density Functions (pmf and pdf) 59
Cumulative Functions (cmf and cdf) 62
Histograms 62
Moments 63
First Moment or Mean 63
Second Central Moment or Variance 64
Population and Sample 66
Other Statistics and Ways of Characterizing a Sample 67
Some Important RV and Distributions 68
Application Examples: Species Diversity 72
Central Limit Theorem 72
Random Number Generation 73
Exercises 74
Computer Session: Probability and Descriptive Statistics 75
Descriptive Statistics: Categorical Data, Table, and Pie Chart 75
Using a Previously Generated Object or a Dataset 78
Summary of Descriptive Statistics and Histogram 78
Density Approximation 81
Theoretical Distribution: Example Binomial Distribution 82
Application Example: Species Diversity 86
Random Number Generation 86
3.9.8Comparing Sample and Theoretical Distributions
Example Binomial 89
Programming Application: Central Limit Theorem 90
Sampling: Function Sample 92
Cleanup and Close R Session 92
Computer Exercises 93
Supplementary Reading 93
Chapter 4 Exploratory Analysis and Introduction to Inferential Statistics 95
4.1 Exploratory Data Analysis (EDA) 95
Index Plot 95
Boxplot 95
Empirical Cumulative Distribution Function (ecdf) 96
Quantile-Quantile (q-q) Plots 98
Combining Plots for Exploratory Data Analysis (EDA) 98
Relationships: Covariance and Correlation 98
4.2.1 Serial Data: Time Series and Autocorrelation 101
Statistical Inference 102
Hypothesis Testing 103
p-Value 105
Power 105
Confidence Intervals 107
Statistical Methods 109
Parametric Methods 110
Z Test or Standard Normal 110
Thef-Test 110
The FTest Ill
Correlation 112
4.6 Nonparametric Methods 1 '2
Mann-Whitney or Wilcoxon Rank Sum Test 112
Wilcoxon Signed Rank Test 112
Spearman Correlation 112
Exercises 1' 3
Computer Session: Exploratory Analysis and Inferential Statistics 113
Create an Example Dataset 1 '3
Index Plot 113
Boxplot 114
Empirical Cumulative Plot 114
Functions 115
Building a Function: Example 115
More on the Standard Normal 116
Quantile-Quantile (q-q) Plots 118
Function to Plot Exploratory Data Analysis (EDA) Graphs 119
Time Series and Autocorrelation Plots 120
Additional Functions for the Rconsole and the R Commander 121
Parametric: One Sample f-Test or Means Test 122
Power Analysis: One Sample f-Test 124
Parametric: Two-Sample f-Test 126
Power Analysis: Two Sample f-Test 128
Using Data Sets from Packages 129
Nonparametric: Wilcoxon Test 130
Bivariate Data and Correlation Test 132
Computer Exercises 135
Supplementary Reading 136
Chapter 5 More on Inferential Statistics: Goodness of Fit, Contingency Analysis,
and Analysis of Variance '37
5.1Goodness of Fit (GOF) 137
Qualitative: Exploratory Analysis 137
x2 (Chi-Square) Test 137
Kolmogorov-Smirnov (K-S) 140
Shapiro-Wilk Test 140
Counts and Proportions 141
Contingency Tables and Cross-Tabulation 141
Analysis of Variance 144
ANOVA One-Way 145
ANOVA Two-Way 148
Factor Interaction in ANOVA Two-Way 149
Nonparametric Analysis of Variance 150
Exercises '5'
Computer Session: More on Inferential Statistics 153
GOF: Exploratory Analysis 153
GOF: Chi-Square Test 154
GOF: Kolmogorov-Smirnov Test 155
GOF: Shapiro-Wilk 156
Count Tests and the Binomial 156
Obtaining a Single Element of a Test Result 157
Comparing Proportions: prop.test 158
Contingency Tables: Direct Input 159
Contingency Tables: Cross-Tabulation 160
ANOVA One-Way 162
ANOVA Two-Way 166
ANOVA Nonparametric: Kruskal-Wallis 169
ANOVA Nonparametric: Friedman 172
ANOVA: Generating Fictional Data for Further Learning 172
Computer Exercises 175
Supplementary Reading 176
Chapter 6 Regression 177
6.1Simple Linear Least Squares Regression 177
Derivatives and Optimization 178
Calculating Regression Coefficients 180
Interpreting the Coefficients Using Sample Means, Variances,and Covariance 183
Regression Coefficients from Expected Values 184
Interpretation of the Error Terms 185
Evaluating Regression Models 188
Regression through the Origin 192
ANOVA as Predictive Tool 195
Nonlinear Regression 196
Log Transform 197
Nonlinear Optimization 197
Polynomial Regression 198
Predicted vs. Observed Plots 198
6.4 Computer .Session: Simple Regression 200
Scatter Plots 200
Simple Linear Regression 202
Nonintercept Model or Regression through the Origin 206
ANOVA One Way: As Linear Model 208
Linear Regression: Lack-of-Fit to Nonlinear Data 211
Nonlinear Regression by Transformation 214
Nonlinear Regression by Optimization 216
Polynomial Regression 219
Predicted vs. Observed Plots 221
Computer Exercises 221
Supplementary Reading 223
Chapter 7 Stochastic or Random Processes and Time Series 225
Stochastic Processes and Time Series: Basics 225
Gaussian 225
Autocovariance and Autocorrelation 227
Periodic Series, Filtering, and Spectral Analysis 231
Poisson Process 238
Marked Poisson Process 241
Simulation 247
Exercises 249
Computer Session: Random Processes and Time Series 250
Gaussian Random Processes 250
Autocorrelation 252
Periodic Process 252
Filtering and Spectrum 253
Sunspots Example 254
Poisson Process 255
Poisson Process Simulation 255
Marked Poisson Process Simulation: Rainfall 256
Computer Exercises 257
Supplementary Reading 258
Chapter 8 Spatial Point Patterns 259
Types of Spatially Explicit Data 259
Types of Spatial Point Patterns 259
Spatial Distribution 259
Testing Spatial Patterns: Cell Count Methods 260
Testing Uniform Patterns 260
Testing for Spatial Randomness 261
Clustered Patterns 263
8.5 Nearest-Neighbor Analysis 264
First-Order Analysis 264
Second-Order Analysis 266
Marked Point Patterns 268
Geostatistics: Regionalized Variables 269
Variograms: Covariance and Semivariance 270
Covariance 271
Semivariance 272
Directions 274
Variogram Models 276
Exponential Model 276
Spherical Model 278
Gaussian Model 278
Linear and Power Models 279
Modeling the Empirical Variogram 280
Exercises 281
Computer Session: Spatial Analysis 284
Packages and Functions 284
File Format 284
Creating a Pattern: Location-Only 285
Generating Patterns with Random Numbers 286
Grid or Quadrat Analysis: Chi-Square Test for Uniformity 288
Grid or Quadrat Analysis: Randomness, Poisson Model 289
Nearest-Neighbor Analysis: G and K Functions 290
Monte Carlo: Nearest-Neighbor Analysis of Uniformity 293
Marked Spatial Patterns: Categorical Marks 294
Marked Spatial Patterns: Continuous Values 298
Marked Patterns: Use Sample Data from sgeostat 301
Computer Exercises 305
Supplementary Reading 306
PART II Matrices, Tempral and Spatial Autoregressive Processes, and Multivariate Analysis
Chapter 9 Matrices and Linear Algebra 309
Matrices 309
Dimension of a Matrix 309
Vectors 310
Square Matrices 310
Trace 311
Symmetric Matrices: Covariance Matrix 311
Identity 312
9.5 Matrix Operations 312
Addition and Subtraction 312
Scalar Multiplication 313
Linear Combination 313
Matrix Multiplication 313
Determinant of a Matrix 315
Matrix Transposition 316.
Major Product 316
Matrix Inversion 317
Solving Systems of Linear Equations 319
Linear Algebra Solution of the Regression Problem 321
Alternative Matrix Approach to Linear Regression 323
Exercises 325
Computer Session: Matrices and Linear Algebra 326
Creating Matrices 326
Operations 327
Other Operations 330
Solving System of Linear Equations 331
Inverse 331
Computer Exercises 332
Supplementary Reading 332
Chapter 10 Multivariate Models 333
10.1 Multiple Linear Regression 333
Mat ri x Approach 333
Population Concepts and Expected Values 338
Evaluation and Diagnostics 339
Variable Selection 340
Multivariate Regression 342
Two-Group Discriminant Analysi 344
Multiple Analysis of Variance (M ANOVA) 349
Exercises 353
10.6 Computer Session: Multivariate Models 355
Multiple Linear Regression 355
Multivariate Regression 359
Two-Group Linear Discriminant Analysis 361
M ANOVA 363
Computer Exercises 365
Functions 365
Supplementary Reading 367
Chapter 11 Dependent Stochastic Processes and Time Series 369
11.1 Markov 369
Dependent Models: Markov Chain 369
Two-Step Rainfall Generation: First Step Markov Sequence 371
Combining Dry/Wet Days with Amount on Wet Days 371
Forest Succession 374
Semi-Markov Processes 378
Autoregressive (AR) Process 381
ARMA and ARIMA Models 387
Exercises 389
Computer Session: Markov Processes and Autoregressive
Time Series 389
Weather Generation: Rainfall Models 389
Semi-Markov 391
AR(p) Modeling and Forecast 392
ARIMA(p, d, q) Modeling and Forecast 395
Computer Exercises 398
SEEG Functions 400
Supplementary Reading 403
Chapter 12 Geostatistics: Kriging 405
Kriging 405
Ordinary Kriging 405
Universal Kriging 413
Data Transformations 414
Exercises 414
Computer Session: Geostatistics, Kriging 415
Ordinary Kriging 415
Universal Kriging 417
Regular Grid Data Files 422
Functions 425
Computer Exercises 428
Supplementary Reading 428
Chapter 13 Spatial Auto-Correlation and Auto-Regression 429
Lattice Data: Spatial Auto-Correlation and Auto-Regression 429
Spatial Structure and Variance Inflation 429
Neighborhood Structure 429
Spatial Auto-Correlation 432
Moran's/ 432
Transformations m 433
Geary's c 434
Spatial Auto-Regression 434
Exercises 436
Computer Session: Spatial Correlation and Regression 437
Packages 437
Mapping Regions 438
Neighborhood Structure 440
Structure Using Distance 441
Structure Based on Borders 445
Spatial Auto-Correlation 446
Spatial Auto-Regression Models 448
Neighborhood Structure Using Tripack 451
Neighborhood Structure for Grid Data 452
Computer Exercises 453
Supplementary Reading 454
Chapter 14 Multivariate Analysis I: Reducing Dimensionality 455
Multivariate Analysis: Eigen-Decomposition 455
Vectors and Linear Transformation 455
Eigenvalues and Eigenvectors 455
Finding Eigenvalues 457
Finding Eigenvectors 458
4.4 Eigen-Decomposition of a Covariance Matrix 459
Covariance Matrix 459
Bivariate Case 461
Principal Components Analysis (PCA) 465
Singular Value Decomposition and Biplots 469
Factor Analysis 472
Correspondence Analysis 475
Exercises 479
Computer Session: Multivariate Analysis, PCA 480
14.10.1 Eigenvalues and Eigenvectors of Covariance Matrices 480
14.10.2 PCA: A Simple 2x2 Example Using Eigenvaluesand Eigenvectors 481
PCA: A 2 x 2 Example 483
PCA Higher-Dimensional Example 485
PCA Using the Rcmdr 486
Factor Analysis 490
Factor Analysis Using Rcmdr 493
Correspondence Analysis 495
Computer Exercises 499
Supplementary Reading 500
Chapter 15 Multivariate Analysis II: Identifying and Developing Relationships among
Observations and Variables 501
Introduction 501
Multigroup Discriminant Analysis (MDA) 501
Canonical Correlation 502
Constrained (or Canonical) Correspondence Analysis (CCA) 505
Cluster Analysis 506
Multidimensional Scaling (MDS) 508
Exercises 509
Computer Session: Multivariate Analysis II 509
Multigroup Linear Discriminant Analysis 509
Canonical Correlation 514
Canonical Correspondence Analysis 515
Cluster Analysis 516
Multidimensional Scaling (MDS) 518
Computer Exercises 520
Supplementary Reading520
Bibliography 521
Index 525