Preface.Acknowledgments.1 Introduction.1.1 Why Spatial Data in Public Health?1.2 Why Statistical Methods for Spatial Data?1.3 Intersection of Three Fields of Study.1.4 Organization of the Book.2 Analyzing Public Health Data.2.1 Observational vs. Experimental Data.2.2 Risk and Rates.2.2.1 Incidence and Prevalence.2.2.2 Risk.2.2.3 Estimating Risk: Rates and Proportions.2.2.4 Relative and Attributable Risks.2.3 Making Rates Comparable: Standardized Rates.2.3.1 Direct Standardization.2.3.2 Indirect Standardization.2.3.3 Direct or Indirect?2.3.4 Standardizing to What Standard?2.3.5 Cautions with Standardized Rates.2.4 Basic Epidemiological Study Designs.2.4.1 Prospective Cohort Studies.2.4.2 Retrospective Case-Control Studies.2.4.3 Other Types of Epidemiological Studies.2.5 Basic Analytic Tool: The Odds Ratio.2.6 Modeling Counts and Rates.2.6.1 Generalized Linear Models.2.6.2 Logistic Regression.2.6.3 Poisson Regression.2.7 Challenges in the Analysis of Observational Data.2.7.1 Bias.2.7.2 Confounding.2.7.3 Effect Modification.2.7.4 Ecological Inference and the Ecological Fallacy.2.8 Additional Topics and Further Reading.2.9 Exercises.3 Spatial Data.3.1 Components of Spatial Data.3.2 An Odyssey into Geodesy.3.2.1 Measuring Location: Geographical Coordinates.3.2.2 Flattening the Globe: Map Projections and Coordinate Systems.3.2.3 Mathematics of Location: Vector and Polygon Geometry.3.3 Sources of Spatial Data.3.3.1 Health Data.3.3.2 Census-Related Data.3.3.3 Geocoding.3.3.4 Digital Cartographic Data.3.3.5 Environmental and Natural Resource Data.3.3.6 Remotely Sensed Data.3.3.7 Digitizing.3.3.8 Collect Your Own!3.4 Geographic Information Systems.3.4.1 Vector and Raster GISs.3.4.2 Basic GIS Operations.3.4.3 Spatial Analysis within GIS.3.5 Problems with Spatial Data and GIS.3.5.1 Inaccurate and Incomplete Databases.3.5.2 Confidentiality.3.5.3 Use of ZIP Codes.3.5.4 Geocoding Issues.3.5.5 Location Uncertainty.4 Visualizing Spatial Data.4.1 Cartography: The Art and Science of Mapmaking.4.2 Types of Statistical Maps.MAP STUDY: Very Low Birth Weights in Georgia Health Care District 9.4.2.1 Maps for Point Features.4.2.2 Maps for Areal Features.4.3 Symbolization.4.3.1 Map Generalization.4.3.2 Visual Variables.4.3.3 Color.4.4 Mapping Smoothed Rates and Probabilities.4.4.1 Locally Weighted Averages.4.4.2 Nonparametric Regression.4.4.3 Empirical Bayes Smoothing.4.4.4 Probability Mapping.4.4.5 Practical Notes and Recommendations.CASE STUDY: Smoothing New York Leukemia Data.4.5 Modifiable Areal Unit Problem.4.6 Additional Topics and Further Reading.4.6.1 Visualization.4.6.2 Additional Types of Maps.4.6.3 Exploratory Spatial Data Analysis.4.6.4 Other Smoothing Approaches.4.6.5 Edge Effects.4.7 Exercises.5 Analysis of Spatial Point Patterns.5.1 Types of Patterns.5.2 Spatial Point Processes.5.2.1 Stationarity and Isotropy.5.2.2 Spatial Poisson Processes and CSR.5.2.3 Hypothesis Tests of CSR via Monte Carlo Methods.5.2.4 Heterogeneous Poisson Processes.5.2.5 Estimating Intensity Functions.DATA BREAK: Early Medieval Grave Sites.5.3 K Function.5.3.1 Estimating the K Function.5.3.2 Diagnostic Plots Based on the K Function.5.3.3 Monte Carlo Assessments of CSR Based on the K Function.DATA BREAK: Early Medieval Grave Sites.5.3.4 Roles of First- and Second-Order Properties.5.4 Other Spatial Point Processes.5.4.1 Poisson Cluster Processes.5.4.2 Contagion/Inhibition Processes.5.4.3 Cox Processes.5.4.4 Distinguishing Processes.5.5 Additional Topics and Further Reading.5.6 Exercises.6 Spatial Clusters of Health Events: Point Data for Cases and Controls.6.1 What Do We Have? Data Types and Related Issues.6.2 What Do We Want? Null and Alternative Hypotheses.6.3 Categorization of Methods.6.4 Comparing Point Process Summaries.6.4.1 Goals.6.4.2 Assumptions and Typical Output.6.4.3 Method: Ratio of Kernel Intensity Estimates.DATA BREAK: Early Medieval Grave Sites.6.4.4 Method: Difference between K Functions.DATA BREAK: Early Medieval Grave Sites.6.5 Scanning Local Rates.6.5.1 Goals.6.5.2 Assumptions and Typical Output.6.5.3 Method: Geographical Analysis Machine.6.5.4 Method: Overlapping Local Case Proportions.DATA BREAK: Early Medieval Grave Sites.6.5.5 Method: Spatial Scan Statistics.DATA BREAK: Early Medieval Grave Sites.6.6 Nearest-Neighbor Statistics.6.6.1 Goals.6.6.2 Assumptions and Typical Output.6.6.3 Method: q Nearest Neighbors of Cases.CASE STUDY: San Diego Asthma.6.7 Further Reading.6.8 Exercises.7 Spatial Clustering of Health Events: Regional Count Data.7.1 What Do We Have and What Do We Want?7.1.1 Data Structure.7.1.2 Null Hypotheses.7.1.3 Alternative Hypotheses.7.2 Categorization of Methods.7.3 Scanning Local Rates.7.3.1 Goals.7.3.2 Assumptions.7.3.3 Method: Overlapping Local Rates.DATA BREAK: New York Leukemia Data.7.3.4 Method: Turnbull et al.'s CEPP.7.3.5 Method: Besag and Newell Approach.7.3.6 Method: Spatial Scan Statistics.7.4 Global Indexes of Spatial Autocorrelation.7.4.1 Goals.7.4.2 Assumptions and Typical Output.7.4.3 Method: Moran's I .7.4.4 Method: Geary's c.7.5 Local Indicators of Spatial Association.7.5.1 Goals.7.5.2 Assumptions and Typical Output.7.5.3 Method: Local Moran's I.7.6 Goodness-of-Fit Statistics.7.6.1 Goals.7.6.2 Assumptions and Typical Output.7.6.3 Method: Pearson's chi2.7.6.4 Method: Tango's Index.7.6.5 Method: Focused Score Tests of Trend.7.7 Statistical Power and Related Considerations.7.7.1 Power Depends on the Alternative Hypothesis.7.7.2 Power Depends on the Data Structure.7.7.3 Theoretical Assessment of Power.7.7.4 Monte Carlo Assessment of Power.7.7.5 Benchmark Data and Conditional Power Assessments.7.8 Additional Topics and Further Reading.7.8.1 Related Research Regarding Indexes of Spatial Association.7.8.2 Additional Approaches for Detecting Clusters and/or Clustering.7.8.3 Space-Time Clustering and Disease Surveillance.7.9 Exercises.8 Spatial Exposure Data.8.1 Random Fields and Stationarity.8.2 Semivariograms.8.2.1 Relationship to Covariance Function and Correlogram.8.2.2 Parametric Isotropic Semivariogram Models.8.2.3 Estimating the Semivariogram.DATA BREAK: Smoky Mountain pH Data.8.2.4 Fitting Semivariogram Models.8.2.5 Anisotropic Semivariogram Modeling.8.3 Interpolation and Spatial Prediction.8.3.1 Inverse-Distance Interpolation.8.3.2 Kriging.CASE STUDY: Hazardous Waste Site Remediation.8.4 Additional Topics and Further Reading.8.4.1 Erratic Experimental Semivariograms.8.4.2 Sampling Distribution of the Classical Semivariogram Estimator.8.4.3 Nonparametric Semivariogram Models.8.4.4 Kriging Non-Gaussian Data.8.4.5 Geostatistical Simulation.8.4.6 Use of Non-Euclidean Distances in Geostatistics.8.4.7 Spatial Sampling and Network Design.8.5 Exercises.9 Linking Spatial Exposure Data to Health Events.9.1 Linear Regression Models for Independent Data.9.1.1 Estimation and Inference.9.1.2 Interpretation and Use with Spatial Data.DATA BREAK: Raccoon Rabies in Connecticut.9.2 Linear Regression Models for Spatially Autocorrelated Data.9.2.1 Estimation and Inference.9.2.2 Interpretation and Use with Spatial Data.9.2.3 Predicting New Observations: Universal Kriging.DATA BREAK: New York Leukemia Data.9.3 Spatial Autoregressive Models.9.3.1 Simultaneous Autoregressive Models.9.3.2 Conditional Autoregressive Models.9.3.3 Concluding Remarks on Conditional Autoregressions.9.3.4 Concluding Remarks on Spatial Autoregressions.9.4 Generalized Linear Models.9.4.1 Fixed Effects and the Marginal Specification.9.4.2 Mixed Models and Conditional Specification.9.4.3 Estimation in Spatial GLMs and GLMMs.DATA BREAK: Modeling Lip Cancer Morbidity in Scotland.9.4.4 Additional Considerations in Spatial GLMs.CASE STUDY: Very Low Birth Weights in Georgia Health Care District 9.9.5 Bayesian Models for Disease Mapping.9.5.1 Hierarchical Structure.9.5.2 Estimation and Inference.9.5.3 Interpretation and Use with Spatial Data.9.6 Parting Thoughts.9.7 Additional Topics and Further Reading.9.7.1 General References.9.7.2 Restricted Maximum Likelihood Estimation.9.7.3 Residual Analysis with Spatially Correlated Error Terms.9.7.4 Two-Parameter Autoregressive Models.9.7.5 Non-Gaussian Spatial Autoregressive Models.9.7.6 Classical/Bayesian GLMMs.9.7.7 Prediction with GLMs.9.7.8 Bayesian Hierarchical Models for Spatial Data.9.8 Exercises.References.Author Index.Subject Index.

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Applied Spatial Statistics for Public Health Data

Assessment of automatic gap fraction estimation of forests from digital hemispherical photography

Spatial relationships between predators and prey have important implications for landscape processes and patterns. Highly mobile oceanic birds and their patchily distributed prey constitute an accessible model system for studying these relationships. High-frequency echosounders can be used together with simultaneous direct visual observations to quantitatively describe the distributions of seabird consumers and their resources over a wide range of spatial scales, yielding information which is rarely available in terrestrial systems.

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Foraging in a fractal environment: Spatial patterns in a marine predator-prey system

[1] The direct comparison of lightning mapping observations by the New Mexico Tech Lightning Mapping Array (LMA) with realistic models of thundercloud electrical structures and lightning discharges represents a useful tool for studies of electrification mechanisms in thunderstorms, initiation and propagation mechanisms of different types of lightning discharges as well as for understanding of electrical and energetic effects of tropospheric thunderstorms on the upper regions of the Earth's atmosphere. This paper presents the formulation of a new three-dimensional probabilistic model for investigating the structure and development of bidirectional positive and negative lightning leaders. The results closely resemble structures observed by the LMA during intracloud discharges. The model represents a synthesis of the original dielectric breakdown model based on fractal approach proposed by Niemeyer et al. (1984) and the equipotential lightning channel hypothesis advanced by Kasemir (1960) and places special emphasis on obtaining self-consistent solutions preserving complete charge neutrality of the discharge trees at any stage of the simulation. A representative simulation run is compared to a typical intracloud discharge measured by LMA in a New Mexico thunderstorm on 31 July 1999. Following the conclusions from Coleman et al. (2003), the comparison of the model and observed discharges reveals that an adequate choice of the electrical structure of the model thundercloud permits the development of a model intracloud discharge reproducing principal features of the observed event including the initial vertical extension of the discharge between the main negative and upper positive charge regions of the thundercloud, and the subsequent horizontal propagations in these regions. Also consistent with observations (e.g., Coleman et al., 2003), negative and positive leaders mainly develop in the upper positive and main negative charge regions, respectively. For the particular model case presented in this paper, the total charge transfer, the vertical dipole moment and the average linear charge density associated with the development of bidirectional structure of leader channels are estimated to be 37.5 C, 122 C·km, and 0.5 mC/m, respectively, in good agreement with related data reported in the refereed literature. The model results also demonstrate that the bulk charge carried by the integral action of positive and negative leaders leads to a significant (up to 80%) reduction of the electric field values inside the thundercloud, significantly below the lightning initiation threshold.

/pdf/three-dimensional-fractal-modeling-of-intracloud-lightning-4a7m9smjt1.pdf

Three‐dimensional fractal modeling of intracloud lightning discharge in a New Mexico thunderstorm and comparison with lightning mapping observations

An iterative wavelet threshold for signal denoising

给出了相似维数、容量维数、盒子维数、信息维数、关联维数、广义维数分形维数等6种分形维数的定义方式,并讨论了它们的应用范围.在此基础上,概括出改变粗视化程度求维数、根据测度关系求维数、根据关联函数求维数、根据分布函数求维数、根据波谱求维数等5种测量维数的方法,为不同领域的科研人员应用维数测量提供了有力工具.

孙博玲

Papers

分形维数（Fractal dimension）及其测量方法