Spatial Autocorrelation and Spatial Filtering Gaining Understanding Through Theory and Scientific Visualization

1 Introduction.- 1.1 Scientific Visualization.- 1.2 What Is Spatial Autocorrelation?.- 1.3 Selected Visualization Tools: An Overview.- 1.4 The Sample Georeferenced Datasets.- 2 Salient Properties of Geographic Connectivity Underlying Spatial Autocorrelation.- 2.1 Eigenfunctions Associated with Geographic Connectivity Matrices.- 2.2 Generalized Eigenvalue Frequency Distributions.- 2.3 The Auto-Gaussian Jacobian Term Normalizing Factor.- 2.4 Eigenfunctions Associated with the GR.- 2.5 Remarks and Discussion.- 3 Sampling Distributions Associated with Spatial Autocorrelation.- 3.1 Samples as Random Permutations of Values across Locations on a Man: Randomization.- 3.2 Simple Random Samples at Each Location on a Map: Unconstrained Selection.- 3.3 Samples as Ordered Random Drawings from a Parent Frequency Distribution: Extending the Permutation Perspective.- 3.4 Samples as Outcomes of a Multivariate Drawing: Extending the Simple Random Samnling Persnective.- 3.5 Effective Sample Size.- 3.6. Remarks and Discussion.- 4 Spatial Filtering.- 4.1 Eigenvector-based Spatial Filtering.- 4.2 Coefficients for Single and Linear Combinations of Distinct Map Patterns.- 4.3 Eigenvector Selection Criteria.- 4.4 Regression Analysis: Standard Errors Based upon Simulation Experiments and Resampling.- 4.5 The MC Local Statistic and Illuminating Diagnostics.- 4.6 Remarks and Discussion.- 5 Spatial Filtering Applications: Selected Interval/Ratio Datasets.- 5.1 Geographic Distributions of Settlement Size in Peru.- 5.2 The Geographic Distribution of Lyme Disease in Georgia.- 5.3 The Geographic Distribution or Biomass in the Hign Peak District.- 5.4 The Geographic Distribution of Agricultural and Topographic Variables in Puerto Rico.- 5.5 Remarks and Discussion.- 6 Spatial Filtering Applications: Selected Counts Datasets.- 6.1 Geographic Distributions of Settlement Counts in Pennsylvania.- 6.2 The Geographic Distribution of Farms in Loiza, Puerto Rico.- 6.3 The Geographic Distribution of Volcanoes in Uganda.- 6.4 The Geographic Distribution of Cholera Deaths in London.- 6.5 The Geographic Distribution of Drumlins in Ireland.- 6.6 Remarks and Discussion.- 7 Spatial Filtering Applications: Selected Percentage Datasets.- 7.1 The Geographic Distribution of the Presence/Absence of Plant Disease in an Agricultural Field.- 7.2 The Geographic Distribution of Plant Disease in an Agricultural Field.- 7.3 The Geographic Distribution of Blood Group A in Eire.- 7.4 The Geographic Distribution of Urbanization across the Island of Puerto Rico.- 7.5 Remarks and Discussion.- 8 Concluding Comments.- 8.1 Spatial Filtering versus Spatial Autoregression.- 8.2 Some Numerical Issues in Spatial Filtering.- 8.3 Stepwise Selection of Eigenvectors for an Auto-Poisson Model.- 8.4 Binomial and Poisson Overdispersion.- 8.5 Future Research: What Next?.- List of Symbols.- List of Tables.- List of Figures.- References.- Author Index.- Place Index.