Geostatistics and Statistical Analysis in Geography

  1. Spatial Interpolation and Surface Estimation
    1. Deterministic Interpolation Methods
      1. Inverse Distance Weighting
        1. Weighting Function
          1. Power Parameter Selection
            1. Search Neighborhood
              1. Limitations and Applications
              2. Trend Surface Analysis
                1. Polynomial Order Selection
                  1. Fitting and Interpretation
                    1. Residual Analysis
                    2. Spline Interpolation
                      1. Regularized Splines
                        1. Tension Splines
                          1. Smoothness and Flexibility
                            1. Barrier Effects
                            2. Triangulated Irregular Networks
                              1. Delaunay Triangulation
                                1. Linear Interpolation
                                  1. Natural Neighbor Interpolation
                                2. Geostatistical Interpolation
                                  1. Principles of Kriging
                                    1. Best Linear Unbiased Estimator
                                      1. Incorporation of Spatial Autocorrelation
                                        1. Kriging Variance
                                          1. Optimality Properties
                                          2. Types of Kriging
                                            1. Simple Kriging
                                              1. Known Mean Assumption
                                                1. Kriging System
                                                  1. Variance Calculation
                                                  2. Ordinary Kriging
                                                    1. Unknown Mean Assumption
                                                      1. Unbiasedness Constraint
                                                        1. Kriging System
                                                        2. Universal Kriging
                                                          1. Trend Modeling
                                                            1. Drift Functions
                                                              1. External Drift
                                                              2. Block Kriging
                                                                1. Prediction over Areas
                                                                  1. Support Effects
                                                                    1. Change of Support
                                                                    2. Co-kriging
                                                                      1. Use of Secondary Variables
                                                                        1. Cross-Correlation
                                                                          1. Undersampling Problem
                                                                          2. Indicator Kriging
                                                                            1. Categorical Data Interpolation
                                                                              1. Threshold Values
                                                                                1. Probability Maps
                                                                                2. Disjunctive Kriging
                                                                                  1. Nonlinear Estimation
                                                                                    1. Hermite Polynomials
                                                                                      1. Change of Support
                                                                                    2. Kriging System of Equations
                                                                                      1. Matrix Formulation
                                                                                        1. Solving for Weights
                                                                                          1. Lagrange Multipliers
                                                                                            1. Numerical Stability
                                                                                          2. Cross-Validation and Model Assessment
                                                                                            1. Validation Techniques
                                                                                              1. Leave-One-Out Cross-Validation
                                                                                                1. K-Fold Cross-Validation
                                                                                                  1. Jackknifing
                                                                                                  2. Error Measures
                                                                                                    1. Mean Prediction Error
                                                                                                      1. Root Mean Square Error
                                                                                                        1. Mean Absolute Error
                                                                                                          1. Standardized Errors
                                                                                                          2. Model Comparison
                                                                                                            1. Information Criteria
                                                                                                              1. Likelihood Ratio Tests
                                                                                                                1. Prediction Intervals

                                                                                                            Previous

                                                                                                            3. Foundations of Geostatistics

                                                                                                            Go to top

                                                                                                            Next

                                                                                                            5. Measuring and Modeling Spatial Autocorrelation