1 Introduction.- 1.1 Scientific Visualization.- 1.2 What Is Spatial Autocorrelation?.- 1.3 Selected Visualization Tools: An Overview.- 1.3.1 Graphical Portrayals of Spatial Autocorrelation.- 1.4 The Sample Georeferenced Datasets.- 1.4.1 Selected Interval/Ratio Datasets.- 1.4.2 Selected Counts Datasets.- 1.4.3 Selected Binomial Datasets.- 2 Salient Properties of Geographic Connectivity Underlying Spatial Autocorrelation.- 2.1 Eigenfunctions Associated with Geographic Connectivity Matrices.- 2.1.1 Eigenvalue Decompositions.- 2.1.2 Eigenvectors Associated with Geographic Connectivity Matrices.- 2.1.3 The Maximum MC Value (MCmax).- 2.1.4 Moments of Eigenvalue Distributions.- 2.2 Generalized Eigenvalue Frequency Distributions.- 2.2.1 The Extreme Eigenvalues of Matrices C and W.- 2.2.2 Spectrum Results for Matrices C and W.- 2.2.3 Spectrum Results for Matrix (I - 11T/n)C(I - 11T/n).- 2.3 The Auto-Gaussian Jacobian Term Normalizing Factor.- 2.3.1 Simplification of the Auto-Gaussian Jacobian Term Based upon Matrix W for a Regular Square Tessellation and the Rook's Definition of Connectivity.- 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.- 3.3.1 The Samnling Distribution fnr MC.- 3.3.2 The Distribution of p for an Auto-normal SAR Model.- 3.4 Samples as Outcomes of a Multivariate Drawing: Extending the Simple Random Samnling Persnective.- 3.4.1 The Auto-normal Model: ML Estimation.- 3.4.2 The Auto-logistic/binomial Model.- 3.4.3 Embedding Spatial Autocorrelation through the Mean Response.- 3.5 Effective Sample Size.- 3.5.1 Estimates Based upon a Single Mean Response.- 3.5.2 Estimates Based upon Multiple Mean Responses.- 3.5.3 Estimates Based upon a Difference of Means for Correlated (Paired) Samples.- 3.5.4 Relationships between Effective Sample Size and the Configuration of Sample Points.- 3.6. Remarks and Discussion.- 4 Spatial Filtering.- 4.1 Eigenvector-based Spatial Filtering.- 4.1.1 Map Patterns Depicted by Eigenvectors of Matrix (I-?C)T(I-? C).- 4.1.2 Similarities with Conventional PCA.- 4.1.3 Orthogonality and Uncorrelatedness of the Eigenvectors.- 4.1.4 Linear Combinations of Eigenvectors of Matrix (I - 11T/n)C(I - 11T/n).- 4.2 Coefficients for Single and Linear Combinations of Distinct Map Patterns.- 4.2.1 Decomposition of Regressor and Regressand Attribute Variables.- 4.2.2 The Sampling Distributions of y? and r.- 4.3 Eigenvector Selection Criteria.- 4.3.1 The Auto-normal Model.- 4.3.2 The Auto-logistic/binomial Model.- 4.3.3 The Auto-Poisson Model.- 4.3.4 The Case of Negative Spatial Autocorrelation.- 4.4 Regression Analysis: Standard Errors Based upon Simulation Experiments and Resampling.- 4.4.1 Simulating Error for Georeferenced Data.- 4.4.2 Bootstrapping Georeferenced Data.- 4.5 The MC Local Statistic and Illuminating Diagnostics.- 4.5.1 The MCis.- 4.5.2 Diagnostics Based upon Eigenvectors of Matrix (I-11T/n)C(I-11T/n).- 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.- 5.5.1 Relationship between the SAR and Eigenvector Spatial Filtering Specifications.- 5.5.2 Computing Back-transformations.- 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.- 8.2.1 Covariation of Spatial Filter and SAR Spatial Autocorrelation Measures.- 8.2.2 Exploding Georeferenced Data with a Spatial Filter When Maps Have Holes or Gaps: Estimating Missing Data Values.- 8.2.3 Rotation and Theoretical Eigenvectors Given by Theorem 2.5 for Regular Square Tessellations Forming Rectangular Regions.- 8.2.4 Effective Sample Size Revisited.- 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.

Scientific visualization may be defined as the transformation of numerical scientific data into informative graphical displays. The text introduces a nonverbal model to subdisciplines that until now has mostly employed mathematical or verbal-conceptual models. The focus is on how scientific visualization can help revolutionize the manner in which the tendencies for (dis)similar numerical values to cluster together in location on a map are explored and analyzed. In doing so, the concept known as spatial autocorrelation - which characterizes these tendencies - is further demystified.