Geostatistics and Statistical Analysis in Geography

  1. Measuring and Modeling Spatial Autocorrelation
    1. Global Measures of Spatial Autocorrelation
      1. Moran's I
        1. Formula and Calculation
          1. Interpretation of Values
            1. Expected Value under Null Hypothesis
              1. Significance Testing
                1. Normal Approximation
                  1. Randomization Tests
                    1. Z-scores and P-values
                  2. Geary's C
                    1. Formula and Calculation
                      1. Interpretation and Comparison with Moran's I
                        1. Sensitivity to Local Variation
                        2. Getis-Ord General G
                          1. Formula and Calculation
                            1. Interpretation
                              1. High-Value vs Low-Value Clustering
                              2. Gamma Index of Spatial Association
                                1. Join Count Statistics
                                  1. Binary Data Analysis
                                    1. Black-Black Joins
                                      1. White-White Joins
                                        1. Black-White Joins
                                      2. Local Indicators of Spatial Association
                                        1. Local Moran's I
                                          1. Calculation and Interpretation
                                            1. Mapping Local Statistics
                                              1. Identifying Spatial Clusters
                                                1. High-High Clusters
                                                  1. Low-Low Clusters
                                                  2. Identifying Spatial Outliers
                                                    1. High-Low Outliers
                                                      1. Low-High Outliers
                                                      2. Multiple Testing Corrections
                                                      3. Getis-Ord Local Statistics
                                                        1. Gi Statistic
                                                          1. Gi* Statistic
                                                            1. Hot Spot Analysis
                                                              1. Clusters of High Values
                                                                1. Statistical Significance
                                                                2. Cold Spot Analysis
                                                                  1. Clusters of Low Values
                                                                    1. Statistical Significance
                                                                  2. Local Geary's C
                                                                    1. Calculation and Interpretation
                                                                      1. Comparison with Local Moran's I
                                                                    2. The Spatial Weights Matrix
                                                                      1. Defining Spatial Relationships
                                                                        1. Concept of Spatial Neighbors
                                                                          1. Neighborhood Structures
                                                                            1. Connectivity Graphs
                                                                            2. Contiguity-Based Weights
                                                                              1. Rook Contiguity
                                                                                1. Shared Edge Neighbors
                                                                                  1. First-Order Contiguity
                                                                                    1. Higher-Order Contiguity
                                                                                    2. Queen Contiguity
                                                                                      1. Shared Edge or Vertex Neighbors
                                                                                        1. Comparison with Rook Contiguity
                                                                                      2. Distance-Based Weights
                                                                                        1. Inverse Distance Weighting
                                                                                          1. Weight Decay Functions
                                                                                            1. Power Parameters
                                                                                            2. Fixed Distance Band
                                                                                              1. Threshold Distance Selection
                                                                                                1. Binary vs Continuous Weights
                                                                                                2. Exponential Distance Decay
                                                                                                  1. Gaussian Distance Decay
                                                                                                  2. K-Nearest Neighbors
                                                                                                    1. Selection of K
                                                                                                      1. Adaptive Neighborhoods
                                                                                                        1. Implications for Analysis
                                                                                                        2. Graph-Based Weights
                                                                                                          1. Gabriel Graph
                                                                                                            1. Relative Neighborhood Graph
                                                                                                              1. Delaunay Triangulation
                                                                                                              2. Row Standardization
                                                                                                                1. Purpose and Calculation
                                                                                                                  1. Effects on Interpretation
                                                                                                                    1. Alternative Standardizations

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                                                                                                                4. Spatial Interpolation and Surface Estimation

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                                                                                                                6. Spatial Regression Analysis