Geostatistics and Statistical Analysis in Geography

  1. Foundations of Geostatistics
    1. The Theory of Regionalized Variables
      1. Concept of Spatial Continuity
        1. Random Function Model
          1. Stochastic Processes in Space
            1. Ergodicity and Stationarity
            2. Stationarity Concepts
              1. First-Order Stationarity
                1. Constant Mean Assumption
                  1. Definition and Implications
                    1. Testing for First-Order Stationarity
                    2. Second-Order Stationarity
                      1. Constant Covariance Structure
                        1. Definition and Assumptions
                          1. Covariance Function Properties
                          2. Intrinsic Stationarity
                            1. Definition and Implications
                              1. Relationship to Second-Order Stationarity
                                1. Practical Applications
                                2. Quasi-Stationarity
                                  1. Local Stationarity
                                    1. Moving Window Approaches
                                  2. The Semivariogram and Covariance Function
                                    1. Understanding Spatial Structure
                                      1. Spatial Autocorrelation in Geostatistics
                                        1. Relationship between Semivariogram and Covariance
                                          1. Interpretation of Spatial Structure
                                          2. Components of the Semivariogram
                                            1. Nugget Effect
                                              1. Measurement Error
                                                1. Micro-scale Variation
                                                  1. Pure Nugget Effect
                                                  2. Sill
                                                    1. Total Variance
                                                      1. Partial Sill
                                                        1. Bounded vs Unbounded Models
                                                        2. Range
                                                          1. Spatial Extent of Correlation
                                                            1. Practical Range
                                                              1. Effective Range
                                                            2. Anisotropy
                                                              1. Geometric Anisotropy
                                                                1. Directional Dependence of Range
                                                                  1. Anisotropy Ratio
                                                                    1. Rotation Angles
                                                                    2. Zonal Anisotropy
                                                                      1. Directional Dependence of Sill
                                                                        1. Nested Structures
                                                                        2. Detection and Modeling
                                                                          1. Directional Semivariograms
                                                                            1. Rose Diagrams
                                                                        3. Fitting a Semivariogram Model
                                                                          1. Experimental Semivariogram Calculation
                                                                            1. Pairwise Difference Calculation
                                                                              1. Lag Distance Selection
                                                                                1. Tolerance Parameters
                                                                                  1. Directional Considerations
                                                                                  2. Theoretical Semivariogram Models
                                                                                    1. Spherical Model
                                                                                      1. Formula and Properties
                                                                                        1. Behavior at Origin
                                                                                          1. Practical Applications
                                                                                          2. Exponential Model
                                                                                            1. Formula and Properties
                                                                                              1. Asymptotic Behavior
                                                                                                1. Practical Applications
                                                                                                2. Gaussian Model
                                                                                                  1. Formula and Properties
                                                                                                    1. Smoothness Properties
                                                                                                      1. Practical Applications
                                                                                                      2. Power Model
                                                                                                        1. Formula and Properties
                                                                                                          1. Fractal Behavior
                                                                                                            1. Practical Applications
                                                                                                            2. Linear Model
                                                                                                              1. Hole Effect Model
                                                                                                              2. Model Selection and Fitting
                                                                                                                1. Least Squares Fitting
                                                                                                                  1. Weighted Least Squares
                                                                                                                    1. Maximum Likelihood Estimation
                                                                                                                      1. Cross-Validation of Models
                                                                                                                        1. Nested Models

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                                                                                                                    2. Descriptive Spatial Statistics

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                                                                                                                    4. Spatial Interpolation and Surface Estimation