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