Data analysis and statistics for geography, environmental science, and engineering

Content: PART I Introduction to Probability, Statistics, Time Series, and Spatial Analysis Introduction Brief History of Statistical and Probabilistic Analysis Computers Applications Types of Variables Probability Theory and Random Variables Methodology Descriptive Statistics Inferential Statistics Predictors, Models, and Regression Time Series Spatial Data Analysis Matrices and Multiple Dimensions Other Approaches: Process-Based Models Baby Steps: Calculations and Graphs Exercises Computer Session: Introduction to R Supplementary Reading Probability Theory Events and Probabilities Algebra of Events Combinations Probability Trees Conditional Probability Testing Water Quality: False Negative and False Positive Bayes' Theorem Generalization of Bayes' Rule to Many Events Bio-Sensing Decision Making Exercises Computer Session: Introduction to Rcmdr, Programming, and Multiple Plots Supplementary Reading Random Variables, Distributions, Moments, and Statistics Random Variables Distributions Moments Some Important RV and Distributions Application Examples: Species Diversity Central Limit Theorem Random Number Generation Exercises Computer Session: Probability and Descriptive Statistics Example Binomial Supplementary Reading Exploratory Analysis and Introduction to Inferential Statistics Exploratory Data Analysis (EDA) Relationships: Covariance and Correlation Statistical Inference Statistical Methods Parametric Methods Nonparametric Methods Exercises Computer Session: Exploratory Analysis and Inferential Statistics Supplementary Reading More on Inferential Statistics: Goodness of Fit, Contingency Analysis, and Analysis of Variance Goodness of Fit (GOF) Counts and Proportions Contingency Tables and Cross-Tabulation Analysis of Variance Exercises Computer Session: More on Inferential Statistics Supplementary Reading Regression Simple Linear Least Squares Regression ANOVA as Predictive Tool Nonlinear Regression Computer Session: Simple Regression Supplementary Reading Stochastic or Random Processes and Time Series Stochastic Processes and Time Series: Basics Gaussian Autocovariance and Autocorrelation Periodic Series, Filtering, and Spectral Analysis Poisson Process Marked Poisson Process Simulation Exercises Computer Session: Random Processes and Time Series Supplementary Reading Spatial Point Patterns Types of Spatially Explicit Data Types of Spatial Point Patterns Spatial Distribution Testing Spatial Patterns: Cell Count Methods Nearest-Neighbor Analysis Marked Point Patterns Geostatistics: Regionalized Variables Variograms: Covariance and Semivariance Directions Variogram Models Exercises Computer Session: Spatial Analysis Supplementary Reading PART II Matrices, Tempral and Spatial Autoregressive Processes, and Multivariate Analysis Matrices and Linear Algebra Matrices Dimension of a Matrix Vectors Square Matrices Matrix Operations Solving Systems of Linear Equations Linear Algebra Solution of the Regression Problem Alternative Matrix Approach to Linear Regression Exercises Computer Session: Matrices and Linear Algebra Supplementary Reading Multivariate Models Multiple Linear Regression Multivariate Regression Two-Group Discriminant Analysis Multiple Analysis of Variance (MANOVA) Exercises Computer Session: Multivariate Models Supplementary Reading Dependent Stochastic Processes and Time Series Markov Semi-Markov Processes Autoregressive (AR) Process ARMA and ARIMA Models Exercises Computer Session: Markov Processes and Autoregressive Time Series Supplementary Reading Geostatistics: Kriging Kriging Ordinary Kriging Universal Kriging Data Transformations Exercises Computer Session: Geostatistics, Kriging Supplementary Reading Spatial Auto-Correlation and Auto-Regression Lattice Data: Spatial Auto-Correlation and Auto-Regression Spatial Structure and Variance Inflation Neighborhood Structure Spatial Auto-Correlation Spatial Auto-Regression Exercises Computer Session: Spatial Correlation and Regression Supplementary Reading Multivariate Analysis I: Reducing Dimensionality Multivariate Analysis: Eigen-Decomposition Vectors and Linear Transformation Eigenvalues and Eigenvectors Eigen-Decomposition of a Covariance Matrix Principal Components Analysis (PCA) Singular Value Decomposition and Biplots Factor Analysis Correspondence Analysis Exercises Computer Session: Multivariate Analysis, PCA Supplementary Reading Multivariate Analysis II: Identifying and Developing Relationships among Observations and Variables Introduction Multigroup Discriminant Analysis (MDA) Canonical Correlation Constrained (or Canonical) Correspondence Analysis (CCA) Cluster Analysis Multidimensional Scaling (MDS) Exercises Computer Session: Multivariate Analysis II Supplementary Reading Bibliography Index