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Modelling Spatial and Spatial-Temporal Data: A Bayesian Approach [Kõva köide]

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(University of Cambridge, UK),
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Modelling Spatial and Spatial-Temporal Data: A Bayesian ApproachSuurem pilt
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Püsilink: https://www.kriso.ee/db/9781482237429.html
Märksõnad:
Modelling Spatial and Spatial-Temporal Data: A Bayesian Approach is aimed at statisticians and quantitative social, economic and public health students and researchers who work with small-area spatial and spatial-temporal data. It assumes a grounding in statistical theory up to the standard linear regression model. The book compares both hierarchical and spatial econometric modelling, providing both a reference and a teaching text with exercises in each chapter. The book provides a fully Bayesian, self-contained, treatment of the underlying statistical theory, with chapters dedicated to substantive applications. The book includes WinBUGS code and R code and all datasets are available online.

Part I covers fundamental issues arising when modelling spatial and spatial-temporal data. Part II focuses on modelling cross-sectional spatial data and begins by describing exploratory methods that help guide the modelling process. There are then two theoretical chapters on Bayesian models and a chapter of applications. Two chapters follow on spatial econometric modelling, one describing different models, the other substantive applications. Part III discusses modelling spatial-temporal data, first introducing models for time series data. Exploratory methods for detecting different types of space-time interaction are presented, followed by two chapters on the theory of space-time separable (without space-time interaction) and inseparable (with space-time interaction) models. An applications chapter includes: the evaluation of a policy intervention; analysing the temporal dynamics of crime hotspots; chronic disease surveillance; and testing for evidence of spatial spillovers in the spread of an infectious disease. A final chapter suggests some future directions and challenges.

Robert Haining is Emeritus Professor in Human Geography, University of Cambridge, England. He is the author of Spatial Data Analysis in the Social and Environmental Sciences (1990) and Spatial Data Analysis: Theory and Practice (2003). He is a Fellow of the RGS-IBG and of the Academy of Social Sciences.

Guangquan Li is Senior Lecturer in Statistics in the Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle, England. His research includes the development and application of Bayesian methods in the social and health sciences. He is a Fellow of the Royal Statistical Society.

Arvustused

"Knowledge on statistical theory and regression concepts are essential to read, comprehend, appreciate, and use the rich contents of this fascinating book. This well-written book is a good source for the Bayesian concepts and methods to practice the spatial-temporal analysis using R and WinBugs codes . . . I recommend this book to economics, health, statistics and computing professionals and researchers." -Ramalingam Shanmugam, Texas State University

"Overall, this book stands out among other spatial statistics books because of its ability to help readers develop practical modeling skills. Specifically, R code snippets are provided when specific R packages or functions are needed to handle geospatial data sets. The impressive number of case studies provide real-world guidance on how to adapt the same modeling strategies, with the accompanyingWinBUGS code, to other data sets. ... In summary, this book is an excellent resource for graduate students, statisticians, and quantitative researchers who are interested in analyzing areal spatial data. The inclusion of both spatial hierarchical models and econometrics models is particularly unique. Finally, the books organization, contents, and writing style also encourage self-learning." -Howard H. Chang in Biometrics, March 2022 "Knowledge on statistical theory and regression concepts are essential to read, comprehend, appreciate, and use the rich contents of this fascinating book. This well-written book is a good source for the Bayesian concepts and methods to practice the spatial-temporal analysis using R and WinBugs codes . . . I recommend this book to economics, health, statistics and computing professionals and researchers." ~ Ramalingam Shanmugam, Texas State University

"All statements in the book are clear and fully understandable for the reader. A large number of examples are accompanied by detailed explanations and R-codes. The book is a very good guide for researchers in the field of spatial and spatial-temporal data modelling for both beginners and professionals"

- Taras Lukashiv, International Society for Clinical Biostatistics, June 2021, Number 71

Preface xix
Acknowledgements xxv
Part I Fundamentals for Modelling Spatial and Spatial-Temporal Data
1 Challenges and Opportunities Analysing Spatial and Spatial-Temporal Data
3(44)
1.1 Introduction
3(1)
1.2 Four Main Challenges When Analysing Spatial and Spatial-Temporal Data
4(10)
1.2.1 Dependency
4(4)
1.2.2 Heterogeneity
8(2)
1.2.3 Data Sparsity
10(2)
1.2.4 Uncertainty
12(2)
1.2.4.1 Data Uncertainty
12(1)
1.2.4.2 Model (or Process) Uncertainty
13(1)
1.2.4.3 Parameter Uncertainty
13(1)
1.3 Opportunities Arising from Modelling Spatial and Spatial-Temporal Data
14(13)
1.3.1 Improving Statistical Precision
14(4)
1.3.2 Explaining Variation in Space and Time
18(9)
1.3.2.1 Example 1: Modelling Exposure-Outcome Relationships
18(2)
1.3.2.2 Example 2: Testing a Conceptual Model at the Small Area Level
20(2)
1.3.2.3 Example 3: Testing for Spatial Spillover (Local Competition) Effects
22(2)
1.3.2.4 Example 4: Assessing the Effects of an Intervention
24(3)
1.3.3 Investigating Space Time Dynamics
27(1)
1.4 Spatial and Spatial-Temporal Models: Bridging between Challenges and Opportunities
27(12)
1.4.1 Statistical Thinking in Analysing Spatial and Spatial-Temporal Data: The Big Picture
27(3)
1.4.2 Bayesian Thinking in a Statistical Analysis
30(3)
1.4.3 Bayesian Hierarchical Models
33(19)
1.4.3.1 Thinking Hierarchically
33(3)
1.4.3.2 Incorporating Spatial and Spatial-Temporal Dependence Structures in a Bayesian Hierarchical Model Using Random Effects
36(1)
1.4.3.3 Information Sharing in a Bayesian Hierarchical Model through Random Effects
37(2)
1.4.4 Bayesian Spatial Econometrics
39(1)
1.5 Concluding Remarks
40(1)
1.6 The Datasets Used in the Book
41(4)
1.7 Exercises
45(2)
2 Concepts for Modelling Spatial and Spatial-Temporal Data: An Introduction to "Spatial Thinking"
47(16)
2.1 Introduction
47(1)
2.2 Mapping Data and Why It Matters
48(4)
2.3 Thinking Spatially
52(4)
2.3.1 Explaining Spatial Variation
52(2)
2.3.2 Spatial Interpolation and Small Area Estimation
54(2)
2.4 Thinking Spatially and Temporally
56(3)
2.4.1 Explaining Space-Time Variation
56(3)
2.4.2 Estimating Parameters for Spatial-Temporal Units
59(1)
2.5 Concluding Remarks
59(1)
2.6 Exercises
60(1)
Appendix: Geographic Information Systems
61(2)
3 The Nature of Spatial and Spatial-Temporal Attribute Data
63(24)
3.1 Introduction
63(1)
3.2 Data Collection Processes in the Social Sciences
63(8)
3.2.1 Natural Experiments
64(3)
3.2.2 Quasi-Experiments
67(1)
3.2.3 Non-Experimental Observational Studies
68(3)
3.3 Spatial and Spatial-Temporal Data: Properties
71(13)
3.3.1 From Geographical Reality to the Spatial Database
71(3)
3.3.2 Fundamental Properties of Spatial and Spatial-Temporal Data
74(2)
3.3.2.1 Spatial and Temporal Dependence
74(1)
3.3.2.2 Spatial and Temporal Heterogeneity
75(1)
3.3.3 Properties Induced by Representational Choices
76(7)
3.3.4 Properties Induced by Measurement Processes
83(1)
3.4 Concluding Remarks
84(1)
3.5 Exercises
84(3)
4 Specifying Spatial Relationships on the Map: The Weights Matrix
87(28)
4.1 Introduction
87(1)
4.2 Specifying Weights Based on Contiguity
88(2)
4.3 Specifying Weights Based on Geographical Distance
90(1)
4.4 Specifying Weights Based on the Graph Structure Associated with a Set of Points
90(2)
4.5 Specifying Weights Based on Attribute Values
92(1)
4.6 Specifying Weights Based on Evidence about Interactions
92(1)
4.7 Row Standardisation
93(2)
4.8 Higher Order Weights Matrices
95(2)
4.9 Choice of W and Statistical Implications
97(8)
4.9.1 Implications for Small Area Estimation
97(5)
4.9.2 Implications for Spatial Econometric Modelling
102(2)
4.9.3 Implications for Estimating the Effects of Observable Covariates on the Outcome
104(1)
4.10 Estimating the W Matrix
105(1)
4.11 Concluding Remarks
106(1)
4.12 Exercises
106(1)
4.13 Appendices
107(1)
Appendix 4.13.1 Building a Geodatabase in R
107(3)
Appendix 4.13.2 Constructing the W Matrix and Accessing Data Stored in a Shapefile
110(5)
5 Introduction to the Bayesian Approach to Regression Modelling with Spatial and Spatial-Temporal Data
115(44)
5.1 Introduction
115(1)
5.2 Introducing Bayesian Analysis
116(5)
5.2.1 Prior, Likelihood and Posterior: What Do These Terms Refer To?
116(4)
5.2.2 Example: Modelling High-Intensity Crime Areas
120(1)
5.3 Bayesian Computation
121(16)
5.3.1 Summarising the Posterior Distribution
121(2)
5.3.2 Integration and Monte Carlo Integration
123(4)
5.3.3 Markov Chain Monte Carlo with Gibbs Sampling
127(2)
5.3.4 Introduction to WinBUGS
129(4)
5.3.5 Practical Considerations when Fitting Models in WinBUGS
133(4)
5.3.5.1 Setting the Initial Values
133(1)
5.3.5.2 Checking Convergence
134(2)
5.3.5.3 Checking Efficiency
136(1)
5.4 Bayesian Regression Models
137(10)
5.4.1 Example I: Modelling Household-Level Income
138(5)
5.4.2 Example II: Modelling Annual Burglary Rates in Small Areas
143(4)
5.5 Bayesian Model Comparison and Model Evaluation
147(1)
5.6 Prior Specifications
148(3)
5.6.1 When We Have Little Prior Information
148(2)
5.6.2 Towards More Informative Priors for Modelling Spatial and Spatial-Temporal Data
150(1)
5.7 Concluding Remarks
151(2)
5.8 Exercises
153(6)
Part II Modelling Spatial Data
6 Exploratory Analysis of Spatial Data
159(54)
6.1 Introduction
159(1)
6.2 Techniques for the Exploratory Analysis of Univariate Spatial Data
160(31)
6.2.1 Mapping
161(4)
6.2.2 Checking for Spatial Trend
165(3)
6.2.3 Checking for Spatial Heterogeneity in the Mean
168(4)
6.2.3.1 Count Data
168(1)
6.2.3.2 A Monte Carlo Test
169(1)
6.2.3.3 Continuous-Valued Data
170(2)
6.2.4 Checking for Global Spatial Dependence (Spatial Autocorrelation)
172(9)
6.2.4.1 The Moran Scatterplot
173(1)
6.2.4.2 The Global Moran's I Statistic
174(3)
6.2.4.3 Other Tests for Assessing Global Spatial Autocorrelation
177(1)
6.2.4.4 The Global Moran's I Applied to Regression Residuals
178(1)
6.2.4.5 The Join-Count Test for Categorical Data
179(2)
6.2.5 Checking for Spatial Heterogeneity in the Spatial Dependence Structure: Detecting Local Spatial Clusters
181(10)
6.2.5.1 The Local Moran's I
182(3)
6.2.5.2 The Multiple Testing Problem When Using Local Moran's I
185(1)
6.2.5.3 Kulldorff's Spatial Scan Statistic
186(5)
6.3 Exploring Relationships between Variables
191(12)
6.3.1 Scatterplots and the Bivariate Moran Scatterplot
191(2)
6.3.2 Quantifying Bivariate Association
193(2)
6.3.2.1 The Clifford-Richardson Test of Bivariate Correlation in the Presence of Spatial Autocorrelation
193(2)
6.3.2.2 Testing for Association "At a Distance" and the Global Bivariate Moran's I
195(1)
6.3.3 Checking for Spatial Heterogeneity in the Outcome-Covariate Relationship: Geographically Weighted Regression (GWR)
195(8)
6.4 Overdispersion and Zero-Inflation in Spatial Count Data
203(4)
6.4.1 Testing for Overdispersion
204(2)
6.4.2 Testing for Zero-Inflation
206(1)
6.5 Concluding Remarks
207(2)
6.6 Exercises
209(1)
Appendix. An R Function to Perform the Zero-Inflation Test by van Den Broek (1995)
210(3)
7 Bayesian Models for Spatial Data I: Non-Hierarchical and Exchangeable Hierarchical Models
213(20)
7.1 Introduction
213(1)
7.2 Estimating Small Area Income: A Motivating Example and Different Modelling Strategies
214(4)
7.2.1 Modelling the 109 Parameters Non-Hierarchically
216(1)
7.2.2 Modelling the 109 Parameters Hierarchically
217(1)
7.3 Modelling the Newcastle Income Data Using Non-Hierarchical Models
218(5)
7.3.1 An Identical Parameter Model Based on Strategy 1
218(2)
7.3.2 An Independent Parameters Model Based on Strategy 2
220(3)
7.4 An Exchangeable Hierarchical Model Based on Strategy 3
223(7)
7.4.1 The Logic of Information Borrowing and Shrinkage
224(1)
7.4.2 Explaining the Nature of Global Smoothing Due to Exchangeability
225(1)
7.4.3 The Variance Partition Coefficient (VPC)
226(2)
7.4.4 Applying an Exchangeable Hierarchical Model to the Newcastle Income Data
228(2)
7.5 Concluding Remarks
230(1)
7.6 Exercises
230(1)
7.7 Appendix: Obtaining the Simulated Household Income Data
231(2)
8 Bayesian Models for Spatial Data II: Hierarchical Models with Spatial Dependence
233(48)
8.1 Introduction
233(1)
8.2 The Intrinsic Conditional Autoregressive (ICAR) Model
234(15)
8.2.1 The ICAR Model Using a Spatial Weights Matrix with Binary Entries
234(11)
8.2.1.1 The WinBUGS Implementation of the ICAR Model
236(2)
8.2.1.2 Applying the ICAR Model Using Spatial Contiguity to the Newcastle Income Data
238(2)
8.2.1.3 Results
240(4)
8.2.1.4 A Summary of the Properties of the ICAR Model Using a Binary Spatial Weights Matrix
244(1)
8.2.2 The ICAR Model with a General Weights Matrix
245(4)
8.2.2.1 Expressing the ICAR Model as a Joint Distribution and the Implied Restriction on W
245(1)
8.2.2.2 The Sum-to-Zero Constraint
246(1)
8.2.2.3 Applying the ICAR Model Using General Weights to the Newcastle Income Data
247(1)
8.2.2.4 Results
248(1)
8.3 The Proper CAR (pCAR) Model
249(7)
8.3.1 Prior Choice for p
251(1)
8.3.2 ICAR or pCAR?
251(2)
8.3.3 Applying the pCAR Model to the Newcastle Income Data
253(1)
8.3.4 Results
253(3)
8.4 Locally Adaptive Models
256(10)
8.4.1 Choosing an Optimal W Matrix from All Possible Specifications
258(1)
8.4.2 Modelling the Elements in the W Matrix
258(4)
8.4.3 Applying Some of the Locally Adaptive Spatial Models to a Subset of the Newcastle Income Data
262(4)
8.5 The Besag, York and Mollie (BYM) Model
266(8)
8.5.1 Two Remarks on Applying the BYM Model in Practice
268(1)
8.5.2 Applying the BYM Model to the Newcastle Income Data
269(5)
8.6 Comparing the Fits of Different Bayesian Spatial Models
274(3)
8.6.1 DIC Comparison
274(2)
8.6.2 Model Comparison Based on the Quality of the MSOA-Level Average Income Estimates
276(1)
8.7 Concluding Remarks
277(2)
8.8 Exercises
279(2)
9 Bayesian Hierarchical Models for Spatial Data: Applications
281(52)
9.1 Introduction
281(1)
9.2 Application 1: Modelling the Distribution of High Intensity Crime Areas in a City
282(14)
9.2.1 Background
282(1)
9.2.2 Data and Exploratory Analysis
283(2)
9.2.3 Methods Discussed in Haining and Law (2007) to Combine the PHIA and EHIA Maps
285(1)
9.2.4 A Joint Analysis of the PHIA and EHIA Data Using the MVCAR Model
286(4)
9.2.5 Results
290(3)
9.2.6 Another Specification of the MVCAR Model and a Limitation of the MVCAR Approach
293(1)
9.2.7 Conclusion and Discussion
293(3)
9.3 Application 2: Modelling the Association Between Air Pollution and Stroke Mortality
296(12)
9.3.1 Background and Data
296(4)
9.3.2 Modelling
300(2)
9.3.3 Interpreting the Statistical Results
302(3)
9.3.4 Conclusion and Discussion
305(3)
9.4 Application 3: Modelling the Village-Level Incidence of Malaria in a Small Region of India
308(13)
9.4.1 Background
308(1)
9.4.2 Data and Exploratory Analysis
308(2)
9.4.3 Model I: A Poisson Regression Model with Random Effects
310(1)
9.4.4 Model II: A Two-Component Poisson Mixture Model
311(2)
9.4.5 Model III: A Two-Component Poisson Mixture Model with Zero-Inflation
313(1)
9.4.6 Results
314(4)
9.4.7 Conclusion and Model Extensions
318(3)
9.5 Application 4: Modelling the Small Area Count of Cases of Rape in Stockholm, Sweden
321(9)
9.5.1 Background and Data
321(1)
9.5.2 Modelling
322(4)
9.5.2.1 A "Whole-Map" Analysis Using Poisson Regression
322(1)
9.5.2.2 A "Localised" Analysis Using Bayesian Profile Regression
323(3)
9.5.3 Results
326(3)
9.5.3.1 "Whole Map" Associations for the Risk Factors
326(1)
9.5.3.2 "Local" Associations for the Risk Factors
326(3)
9.5.4 Conclusions
329(1)
9.6 Exercises
330(3)
10 Spatial Econometric Models
333(40)
10.1 Introduction
333(1)
10.2 Spatial Econometric Models
334(12)
10.2.1 Three Forms of Spatial Spillover
334(1)
10.2.2 The Spatial Lag Model (SLM)
335(4)
10.2.2.1 Formulating the Model
335(1)
10.2.2.2 An Example of the SLM
336(1)
10.2.2.3 The Reduced Form of the SLM and the Constraint on S
337(1)
10.2.2.4 Specification of the Spatial Weights Matrix
338(1)
10.2.2.5 Issues with Model Fitting and Interpreting Coefficients
339(1)
10.2.3 The Spatially-Lagged Covariates Model (SLX)
339(1)
10.2.3.1 Formulating the Model
339(1)
10.2.3.2 An Example of the SLX Model
340(1)
10.2.4 The Spatial Error Model (SEM)
340(1)
10.2.5 The Spatial Durbin Model (SDM)
341(1)
10.2.5.1 Formulating the Model
341(1)
10.2.5.2 Relating the SDM Model to the Other Three Spatial Econometric Models
342(1)
10.2.6 Prior Specifications
342(1)
10.2.7 An Example: Modelling Cigarette Sales in 46 US States
343(3)
10.2.7.1 Data Description, Exploratory Analysis and Model Specifications
343(2)
10.2.7.2 Results
345(1)
10.3 Interpreting Covariate Effects
346(10)
10.3.1 Definitions of the Direct, Indirect and Total Effects of a Covariate
346(1)
10.3.2 Measuring Direct and Indirect Effects without the SAR Structure on the Outcome Variables
347(3)
10.3.2.1 For the LM and SEM Models
347(1)
10.3.2.2 For the SLX Model
347(3)
10.3.3 Measuring Direct and Indirect Effects When the Outcome Variables are Modelled by the SAR Structure
350(5)
10.3.3.1 Understanding Direct and Indirect Effects in the Presence of Spatial Feedback
350(1)
10.3.3.2 Calculating the Direct and Indirect Effects in the Presence of Spatial Feedback
351(1)
10.3.3.3 Some Properties of Direct and Indirect Effects
351(3)
10.3.3.4 A Property (Limitation) of the Average Direct and Average Indirect Effects Under the SLM Model
354(1)
10.3.3.5 Summary
354(1)
10.3.4 The Estimated Effects from the Cigarette Sales Data
355(1)
10.4 Model Fitting in WinBUGS
356(9)
10.4.1 Derivation of the Likelihood Function
357(4)
10.4.2 Simplifications to the Likelihood Computation
361(1)
10.4.3 The Zeros-Trick in WinBUGS
361(1)
10.4.4 Calculating the Covariate Effects in WinBUGS
362(3)
10.5 Concluding Remarks
365(5)
10.5.1 Other Spatial Econometric Models and the Two Problems of Identifiability
365(2)
10.5.2 Comparing the Hierarchical Modelling Approach and the Spatial Econometric Approach: A Summary
367(3)
10.6 Exercises
370(3)
11 Spatial Econometric Modelling: Applications
373(17)
11.1 Application 1: Modelling the Voting Outcomes at the Local Authority District Level in England from the 2016 EU Referendum
373(9)
11.1.1 Introduction
373(1)
11.1.2 Data
374(1)
11.1.3 Exploratory Data Analysis
375(1)
11.1.4 Modelling Using Spatial Econometric Models
375(3)
11.1.5 Results
378(3)
11.1.6 Conclusion and Discussion
381(1)
11.2 Application 2: Modelling Price Competition Between Petrol Retail Outlets in a Large City
382(6)
11.2.1 Introduction
382(1)
11.2.2 Data
383(1)
11.2.3 Exploratory Data Analysis
383(1)
11.2.4 Spatial Econometric Modelling and Results
384(1)
11.2.5 A Spatial Hierarchical Model with t4 Likelihood
385(3)
11.2.6 Conclusion and Discussion
388(1)
11.3 Final Remarks on Spatial Econometric Modelling of Spatial Data
388(1)
11.4 Exercises
389(1)
Appendix: Petrol Retail Price Data
390(5)
Part III Modelling Spatial-Temporal Data
12 Modelling Spatial-Temporal Data: An Introduction
395(44)
12.1 Introduction
395(3)
12.2 Modelling Annual Counts of Burglary Cases at the Small Area Level: A Motivating Example and Frameworks for Modelling Spatial-Temporal Data
398(3)
12.3 Modelling Small Area Temporal Data
401(33)
12.3.1 Issues to Consider When Modelling Temporal Patterns in the Small Area Setting
403(3)
12.3.1.1 Issues Relating to Temporal Dependence
403(1)
12.3.1.2 Issues Relating to Temporal Heterogeneity and Spatial Heterogeneity in Modelling Small Area Temporal Patterns
404(1)
12.3.1.3 Issues Relating to Flexibility of a Temporal Model
404(2)
12.3.2 Modelling Small Area Temporal Patterns: Setting the Scene
406(1)
12.3.3 A Linear Time Trend Model
407(9)
12.3.3.1 Model Formulations
407(4)
12.3.3.2 Modelling Trends in the Peterborough Burglary Data
411(5)
12.3.4 Random Walk Models
416(10)
12.3.4.1 Model Formulations
417(1)
12.3.4.2 The RW1 Model: Its Formulation Via the Full Conditionals and Its Properties
418(3)
12.3.4.3 WinBUGS Implementation of the RW1 Model
421(1)
12.3.4.4 Example: Modelling Burglary Trends Using the Peterborough Data
421(3)
12.3.4.5 The Random Walk Model of Order 2
424(2)
12.3.5 Interrupted Time Series (ITS) Models
426(22)
12.3.5.1 Quasi-Experimental Designs and the Purpose of ITS Modelling
426(2)
12.3.5.2 Model Formulations
428(1)
12.3.5.3 WinBUGS Implementation
429(3)
12.3.5.4 Results
432(2)
12.4 Concluding Remarks
434(1)
12.5 Exercises
435(1)
Appendix: Three Different Forms for Specifying the Impact Function f
436(3)
13 Exploratory Analysis of Spatial-Temporal Data
439(26)
13.1 Introduction
439(1)
13.2 Patterns of Spatial-Temporal Data
440(3)
13.3 Visualising Spatial-Temporal Data
443(5)
13.4 Tests of Space Time Interaction
448(15)
13.4.1 The Knox Test
449(5)
13.4.1.1 An Instructive Example of the Knox Test and Different Methods to Derive a p-Value
451(2)
13.4.1.2 Applying the Knox Test to the Malaria Data
453(1)
13.4.2 Kulldorff's Space Time Scan Statistic
454(5)
13.4.2.1 Application: The Simulated Small Area COPD Mortality Data
456(3)
13.4.3 Assessing Space Time Interaction in the Form of Varying Local Time Trend Patterns
459(8)
13.4.3.1 Exploratory Analysis of the Local Trends in the Peterborough Burglary Data
460(1)
13.4.3.2 Exploratory Analysis of the Local Time Trends in the England COPD Mortality Data
460(3)
13.5 Concluding Remarks
463(1)
13.6 Exercises
464(1)
14 Bayesian Hierarchical Models for Spatial-Temporal Data I: Space-Time Separable Models
465(16)
14.1 Introduction
465(1)
14.2 Estimating Small Area Burglary Rates Over Time: Setting the Scene
465(2)
14.3 The Space-Time Separable Modelling Framework
467(11)
14.3.1 Model Formulations
467(2)
14.3.2 Do We Combine the Space and Time Components Additively or Multiplicatively?
469(1)
14.3.3 Analysing the Peterborough Burglary Data Using a Space-Time Separable Model
470(4)
14.3.4 Results
474(4)
14.4 Concluding Remarks
478(1)
14.5 Exercises
479(2)
15 Bayesian Hierarchical Models for Spatial-Temporal Data II: Space-Time Inseparable Models
481(36)
15.1 Introduction
481(1)
15.2 From Space-Time Separability to Space-Time Inseparability: The Big Picture
481(3)
15.3 Type I Space-Time Interaction
484(2)
15.3.1 Example: A Space-Time Model with Type I Space-Time Interaction
484(2)
15.3.2 WinBUGS Implementation
486(1)
15.4 Type II Space-Time Interaction
486(4)
15.4.1 Example: Two Space-Time Models with Type II Space-Time Interaction
489(1)
15.4.2 WinBUGS Implementation
490(1)
15.5 Type III Space-Time Interaction
490(3)
15.5.1 Example: A Space-Time Model with Type III Space-Time Interaction
491(1)
15.5.2 WinBUGS Implementation
492(1)
15.6 Results from Analysing the Peterborough Burglary Data
493(5)
15.7 Type IV Space-Time Interaction
498(15)
15.7.1 Strategy 1: Extending Type II to Type IV
499(2)
15.7.2 Strategy 2: Extending Type III to Type IV
501(3)
15.7.2.1 Examples of Strategy 2
502(2)
15.7.3 Strategy 3: Clayton's Rule
504(8)
15.7.3.1 Structure Matrices and Gaussian Markov Random Fields
505(1)
15.7.3.2 Taking the Kronecker Product
506(2)
15.7.3.3 Exploring the Induced Space-Time Dependence Structure via the Full Conditionals
508(4)
15.7.4 Summary on Type IV Space-Time Interaction
512(1)
15.8 Concluding Remarks
513(2)
15.9 Exercises
515(2)
16 Applications in Modelling Spatial-Temporal Data
517(48)
16.1 Introduction
517(1)
16.2 Application 1: Evaluating a Targeted Crime Reduction Intervention
518(9)
16.2.1 Background and Data
518(2)
16.2.2 Constructing Different Control Groups
520(1)
16.2.3 Evaluation Using ITS
521(2)
16.2.4 WinBUGS Implementation
523(1)
16.2.5 Results
523(3)
16.2.6 Some Remarks
526(1)
16.3 Application 2: Assessing the Stability of Risk in Space and Time
527(12)
16.3.1 Studying the Temporal Dynamics of Crime Hotspots and Coldspots: Background, Data and the Modelling Idea
527(3)
16.3.2 Model Formulations
530(1)
16.3.3 Classification of Areas
531(1)
16.3.4 Model Implementation and Area Classification
532(3)
16.3.5 Interpreting the Statistical Results
535(4)
16.4 Application 3: Detecting Unusual Local Time Patterns in Small Area Data
539(11)
16.4.1 Small Area Disease Surveillance: Background and Modelling Idea
539(1)
16.4.2 Model Formulation
540(3)
16.4.3 Detecting Unusual Areas with a Control of the False Discovery Rate
543(1)
16.4.4 Fitting BaySTDetect in WinBUGS
543(3)
16.4.5 A Simulated Dataset to Illustrate the Use of BaySTDetect
546(1)
16.4.6 Results from the Simulated Dataset
546(2)
16.4.7 General Results from Li et al. (2012) and an Extension of BaySTDetect
548(2)
16.5 Application 4: Investigating the Presence of Spatial-Temporal Spillover Effects on Village-Level Malaria Risk in Kalaburagi, Karnataka, India
550(8)
16.5.1 Background and Study Objective
550(1)
16.5.2 Data
551(1)
16.5.3 Modelling
552(1)
16.5.4 Results
553(3)
16.5.5 Concluding Remarks
556(2)
16.6 Conclusions
558(2)
16.7 Exercises
560(5)
Part IV Addendum
17 Modelling Spatial and Spatial-Temporal Data: Future Agendas?
565(12)
17.1 Topic 1: Modelling Multiple Related Outcomes Over Space and Time
565(2)
17.2 Topic 2: Joint Modelling of Georeferenced Longitudinal and Time-to-Event Data
567(1)
17.3 Topic 3: Multiscale Modelling
567(1)
17.4 Topic 4: Using Survey Data for Small Area Estimation
568(3)
17.5 Topic 5: Combining Data at Both Aggregate and Individual Levels to Improve Ecological Inference
571(1)
17.6 Topic 6: Geostatistical Modelling
572(3)
17.6.1 Spatial Dependence
573(1)
17.6.2 Mapping to Reduce Visual Bias
574(1)
17.6.3 Modelling Scale Effects
574(1)
17.7 Topic 7: Modelling Count Data in Spatial Econometrics
575(1)
17.8 Topic 8: Computation
575(2)
References 577(20)
Index 597
Robert Haining is Emeritus Professor in Human Geography, University of Cambridge, England. He is the author of Spatial Data Analysis in the Social and Environmental Sciences (1990) and Spatial Data Analysis: Theory and Practice (2003). He is a Fellow of the RGS-IBG and of the Academy of Social Sciences.

Guangquan Li is Senior Lecturer in Statistics in the Department of Mathematics, Physics and Electrical Engineering, Northumbria University, Newcastle, England. His research includes the development and application of Bayesian methods in the social and health sciences. He is a Fellow of the Royal Statistical Society.