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Xuehua Han - One of the best experts on this subject based on the ideXlab platform.
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using monte carlo simulation to improve the performance of Semivariograms for choosing the remote sensing imagery resolution for natural resource surveys case study on three counties in east central and west china
ISPRS international journal of geo-information, 2018Co-Authors: Juanle Wang, Junxiang Zhu, Xuehua HanAbstract:Semivariograms have been widely used in research to obtain optimal resolutions for ground features. To obtain the semivariogram curve and its attributes (range and sill), parameters including sample size (SS), maximum distance (MD), and group number (GN) have to be defined, as well as a mathematic model for fitting the curve. However, a clear guide on parameter setting and model selection is currently not available. In this study, a Monte Carlo simulation-based approach (MCS) is proposed to enhance the performance of Semivariograms by optimizing the parameters, and case studies in three regions are conducted to determine the optimal resolution for natural resource surveys. Those parameters are optimized one by one through several rounds of MCS. The result shows that exponential model is better than sphere model; sample size has a positive relationship with R2, while the group number has a negative one; increasing the simulation number could improve the accuracy of estimation; and eventually the optimized parameters improved the performance of semivariogram. In case study, the average sizes for three general ground features (grassland, farmland, and forest) of three counties (Ansai, Changdu, and Taihe) in different geophysical locations of China were acquired and compared, and imagery with an appropriate resolution is recommended. The results show that the ground feature sizes acquired by means of MCS and optimized parameters in this study match well with real land cover patterns.
Juanle Wang - One of the best experts on this subject based on the ideXlab platform.
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using monte carlo simulation to improve the performance of Semivariograms for choosing the remote sensing imagery resolution for natural resource surveys case study on three counties in east central and west china
ISPRS international journal of geo-information, 2018Co-Authors: Juanle Wang, Junxiang Zhu, Xuehua HanAbstract:Semivariograms have been widely used in research to obtain optimal resolutions for ground features. To obtain the semivariogram curve and its attributes (range and sill), parameters including sample size (SS), maximum distance (MD), and group number (GN) have to be defined, as well as a mathematic model for fitting the curve. However, a clear guide on parameter setting and model selection is currently not available. In this study, a Monte Carlo simulation-based approach (MCS) is proposed to enhance the performance of Semivariograms by optimizing the parameters, and case studies in three regions are conducted to determine the optimal resolution for natural resource surveys. Those parameters are optimized one by one through several rounds of MCS. The result shows that exponential model is better than sphere model; sample size has a positive relationship with R2, while the group number has a negative one; increasing the simulation number could improve the accuracy of estimation; and eventually the optimized parameters improved the performance of semivariogram. In case study, the average sizes for three general ground features (grassland, farmland, and forest) of three counties (Ansai, Changdu, and Taihe) in different geophysical locations of China were acquired and compared, and imagery with an appropriate resolution is recommended. The results show that the ground feature sizes acquired by means of MCS and optimized parameters in this study match well with real land cover patterns.
Jackson Jr B Smith - One of the best experts on this subject based on the ideXlab platform.
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Semivariograms from a forest transect gap model compared with remotely sensed data
Journal of Vegetation Science, 1992Co-Authors: John F Weishampel, Dean L Urban, Herman H Shugart, Jackson Jr B SmithAbstract:A spatially linked version of a forest gap model, ZELIG, parameterized for the H. J. Andrews Experimental Forest, Oregon, was used to generate structural properties (i.e. biomass, leaf area, and maximum tree height) of young (80 yr), mature (140 yr), and old-growth (450 yr) Pseudotsuga menziesii (Douglas fir) forests. Semivariograms were pro- duced at 10 and 30 m resolution to describe the spatio-tempo- ral patterns of variation of the simulated structural features along a 5 km transect of contiguous 10 m x 10 m grid cells. These Semivariograms from the simulations were compared with Semivariograms from matrices of pixel digital values obtained from aerial videography of similarly aged stands. Although autocorrelative spatial patterning was absent from both the remotely sensed imagery (except at < 20 m for the 450 yr stand) and the model output, the pixel-to-pixel and plot-to- plot variances exhibited similar patterns across the chronosequence at both resolutions. This suggests that gap models are able to capture temporal aspects of landscape dynamics associated with canopy texture of Pacific Northwest forests.
Carol A Gotway - One of the best experts on this subject based on the ideXlab platform.
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statistical methods for spatial data analysis
2004Co-Authors: Oliver Schabenberger, Carol A GotwayAbstract:INTRODUCTION The Need for Spatial Analysis Types of Spatial Data Autocorrelation-Concept and Elementary Measures Autocorrelation Functions The Effects of Autocorrelation on Statistical Inference Chapter Problems SOME THEORY ON RANDOM FIELDS Stochastic Processes and Samples of Size One Stationarity, Isotropy, and Heterogeneity Spatial Continuity and Differentiability Random Fields in the Spatial Domain Random Fields in the Frequency Domain Chapter Problems MAPPED POINT PATTERNS Random, Aggregated, and Regular Patterns Binomial and Poisson Processes Testing for Complete Spatial Randomness Second-Order Properties of Point Patterns The Inhomogeneous Poisson Process Marked and Multivariate Point Patterns Point Process Models Chapter Problems SEMIVARIOGRAM AND COVARIANCE FUNCTION ANALYSIS AND ESTIMATION Introduction Semivariogram and Covariogram Covariance and Semivariogram Models Estimating the Semivariogram Parametric Modeling Nonparametric Estimation and Modeling Estimation and Inference in the Frequency Domain On the Use of Non-Euclidean Distances in Geostatistics Supplement: Bessel Functions Chapter Problems SPATIAL PREDICTION AND KRIGING Optimal Prediction in Random Fields Linear Prediction-Simple and Ordinary Kriging Linear Prediction with a Spatially Varying Mean Kriging in Practice Estimating Covariance Parameters Nonlinear Prediction Change of Support On the Popularity of the Multivariate Gaussian Distribution Chapter Problems SPATIAL REGRESSION MODELS Linear Models with Uncorrelated Errors Linear Models with Correlated Errors Generalized Linear Models Bayesian Hierarchical Models Chapter Problems SIMULATION OF RANDOM FIELDS Unconditional Simulation of Gaussian Random Fields Conditional Simulation of Gaussian Random Fields Simulated Annealing Simulating from Convolutions Simulating Point Processes Chapter Problems NON-STATIONARY COVARIANCE Types of Non-Stationarity Global Modeling Approaches Local Stationarity SPATIO-TEMPORAL PROCESSES A New Dimension Separable Covariance Functions Non-Separable Covariance Functions The Spatio-Temporal Semivariogram Spatio-Temporal Point Processes
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statistical methods for spatial data analysis
2004Co-Authors: Oliver Schabenberger, Carol A GotwayAbstract:INTRODUCTION The Need for Spatial Analysis Types of Spatial Data Autocorrelation-Concept and Elementary Measures Autocorrelation Functions The Effects of Autocorrelation on Statistical Inference Chapter Problems SOME THEORY ON RANDOM FIELDS Stochastic Processes and Samples of Size One Stationarity, Isotropy, and Heterogeneity Spatial Continuity and Differentiability Random Fields in the Spatial Domain Random Fields in the Frequency Domain Chapter Problems MAPPED POINT PATTERNS Random, Aggregated, and Regular Patterns Binomial and Poisson Processes Testing for Complete Spatial Randomness Second-Order Properties of Point Patterns The Inhomogeneous Poisson Process Marked and Multivariate Point Patterns Point Process Models Chapter Problems SEMIVARIOGRAM AND COVARIANCE FUNCTION ANALYSIS AND ESTIMATION Introduction Semivariogram and Covariogram Covariance and Semivariogram Models Estimating the Semivariogram Parametric Modeling Nonparametric Estimation and Modeling Estimation and Inference in the Frequency Domain On the Use of Non-Euclidean Distances in Geostatistics Supplement: Bessel Functions Chapter Problems SPATIAL PREDICTION AND KRIGING Optimal Prediction in Random Fields Linear Prediction-Simple and Ordinary Kriging Linear Prediction with a Spatially Varying Mean Kriging in Practice Estimating Covariance Parameters Nonlinear Prediction Change of Support On the Popularity of the Multivariate Gaussian Distribution Chapter Problems SPATIAL REGRESSION MODELS Linear Models with Uncorrelated Errors Linear Models with Correlated Errors Generalized Linear Models Bayesian Hierarchical Models Chapter Problems SIMULATION OF RANDOM FIELDS Unconditional Simulation of Gaussian Random Fields Conditional Simulation of Gaussian Random Fields Simulated Annealing Simulating from Convolutions Simulating Point Processes Chapter Problems NON-STATIONARY COVARIANCE Types of Non-Stationarity Global Modeling Approaches Local Stationarity SPATIO-TEMPORAL PROCESSES A New Dimension Separable Covariance Functions Non-Separable Covariance Functions The Spatio-Temporal Semivariogram Spatio-Temporal Point Processes
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applied spatial statistics for public health data
2004Co-Authors: Lance A Waller, Carol A GotwayAbstract: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
2004Co-Authors: Lance A Waller, Carol A GotwayAbstract: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.
Uwe Haberlandt - One of the best experts on this subject based on the ideXlab platform.
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spatial interpolation of hourly rainfall effect of additional information variogram inference and storm properties
Hydrology and Earth System Sciences, 2011Co-Authors: A Verworn, Uwe HaberlandtAbstract:Abstract. Hydrological modelling of floods relies on precipitation data with a high resolution in space and time. A reliable spatial representation of short time step rainfall is often difficult to achieve due to a low network density. In this study hourly precipitation was spatially interpolated with the multivariate geostatistical method kriging with external drift (KED) using additional information from topography, rainfall data from the denser daily networks and weather radar data. Investigations were carried out for several flood events in the time period between 2000 and 2005 caused by different meteorological conditions. The 125 km radius around the radar station Ummendorf in northern Germany covered the overall study region. One objective was to assess the effect of different approaches for estimation of Semivariograms on the interpolation performance of short time step rainfall. Another objective was the refined application of the method kriging with external drift. Special attention was not only given to find the most relevant additional information, but also to combine the additional information in the best possible way. A multi-step interpolation procedure was applied to better consider sub-regions without rainfall. The impact of different semivariogram types on the interpolation performance was low. While it varied over the events, an averaged semivariogram was sufficient overall. Weather radar data were the most valuable additional information for KED for convective summer events. For interpolation of stratiform winter events using daily rainfall as additional information was sufficient. The application of the multi-step procedure significantly helped to improve the representation of fractional precipitation coverage.
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geostatistical interpolation of hourly precipitation from rain gauges and radar for a large scale extreme rainfall event
Journal of Hydrology, 2007Co-Authors: Uwe HaberlandtAbstract:Summary The methods kriging with external drift (KED) and indicator kriging with external drift (IKED) are used for the spatial interpolation of hourly rainfall from rain gauges using additional information from radar, daily precipitation of a denser network, and elevation. The techniques are illustrated using data from the storm period of the 10th to the 13th of August 2002 that led to the extreme flood event in the Elbe river basin in Germany. Cross-validation is applied to compare the interpolation performance of the KED and IKED methods using different additional information with the univariate reference methods nearest neighbour (NN) or Thiessen polygons, inverse square distance weighting (IDW), ordinary kriging (OK) and ordinary indicator kriging (IK). Special attention is given to the analysis of the impact of the semivariogram estimation on the interpolation performance. Hourly and average Semivariograms are inferred from daily, hourly and radar data considering either isotropic or anisotropic behaviour using automatic and manual fitting procedures. The multivariate methods KED and IKED clearly outperform the univariate ones with the most important additional information being radar, followed by precipitation from the daily network and elevation, which plays only a secondary role here. The best performance is achieved when all additional information are used simultaneously with KED. The indicator-based kriging methods provide, in some cases, smaller root mean square errors than the methods, which use the original data, but at the expense of a significant loss of variance. The impact of the semivariogram on interpolation performance is not very high. The best results are obtained using an automatic fitting procedure with isotropic variograms either from hourly or radar data.
