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E-grāmata: Handbook of Environmental and Ecological Statistics

Edited by (Duke University, Durham, North Carolina), Edited by , Edited by (North Carolina State University, Raleigh), Edited by
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This handbook focuses on the enormous literature applying statistical methodology and modelling to environmental and ecological processes. The 21st century statistics community has become increasingly interdisciplinary, bringing a large collection of modern tools to all areas of application in environmental processes. In addition, the environmental community has substantially increased its scope of data collection including observational data, satellite-derived data, and computer model output. The resultant impact in this latter community has been substantial; no longer are simple regression and analysis of variance methods adequate. The contribution of this handbook is to assemble a state-of-the-art view of this interface.

Features:











An internationally regarded editorial team.





A distinguished collection of contributors.





A thoroughly contemporary treatment of a substantial interdisciplinary interface.





Written to engage both statisticians as well as quantitative environmental researchers.





34 chapters covering methodology, ecological processes, environmental exposure, and statistical methods in climate science.

Recenzijas

"This is an extremely well-composed book, offering an interdisciplinary exposure to the concepts and methods that are very valuable to perform environmental and ecological data analysis. The contributors are recognized experts in the topics of their writing...Noteworthy features in this book are introducing uncertainty, anisotropy and non-stationarity, threshold exceedance, coenospace, stochasticity, tail-down models, entropy-based design among others...I highly recommend this book to environmental, climate, statistics and computing researchers and practicing professionals." - Ramalingam Shanmugam, JSCS, Aug 2020

Preface xxi
1 Introduction
1(6)
Alan E. Gelfand
Montserrat Fuentes
Jennifer Hoeting
Richard L. Smith
I Methodology for Statistical Analysis of Environmental Processes 7(268)
2 Modeling for environmental and ecological processes
9(24)
Alan E. Gelfand
2.1 Introduction
10(1)
2.2 Stochastic modeling
10(3)
2.3 Basics of Bayesian inference
13(3)
2.3.1 Priors
14(1)
2.3.2 Posterior inference
15(1)
2.3.3 Bayesian computation
15(1)
2.4 Hierarchical modeling
16(3)
2.4.1 Introducing uncertainty
17(1)
2.4.2 Random effects and missing data
18(1)
2.5 Latent variables
19(1)
2.6 Mixture models
20(1)
2.7 Random effects
21(1)
2.8 Dynamic models
22(1)
2.9 Model adequacy
23(2)
2.10 Model comparison
25(3)
2.10.1 Bayesian model comparison
25(2)
2.10.2 Model comparison in predictive space
27(1)
2.11 Summary
28(5)
3 Time series methodology
33(24)
Peter F. Craigmile
3.1 Introduction
33(2)
3.2 Time series processes
35(1)
3.3 Stationary processes
35(4)
3.3.1 Filtering preserves stationarity
36(1)
3.3.2 Classes of stationary processes
36(1)
3.3.2.1 IID noise and white noise
37(1)
3.3.2.2 Linear processes
37(1)
3.3.2.3 Autoregressive moving average processes
37(2)
3.4 Statistical inference for stationary series
39(9)
3.4.1 Estimating the process mean
39(1)
3.4.2 Estimating the ACVF and ACF
40(1)
3.4.3 Prediction and forecasting
41(1)
3.4.4 Using measures of correlation for ARMA model identification
42(1)
3.4.5 Parameter estimation
43(2)
3.4.6 Model assessment and comparison
45(1)
3.4.7 Statistical inference for the Canadian lynx series
46(2)
3.5 Nonstationary time series
48(2)
3.5.1 A classical decomposition for nonstationary processes
48(1)
3.5.2 Stochastic representations of nonstationarity
49(1)
3.6 Long memory processes
50(1)
3.7 Changepoint methods
50(1)
3.8 Discussion and conclusions
51(6)
4 Dynamic models
57(24)
Alexandra M. Schmidt
Hedibert F. Lopes
4.1 Introduction
57(1)
4.2 Univariate Normal Dynamic Linear Models (NDLM)
58(8)
4.2.1 Forward learning: the Kalman filter
59(1)
4.2.2 Backward learning: the Kalman smoother
60(2)
4.2.3 Integrated likelihood
62(1)
4.2.4 Some properties of NDLMs
62(1)
4.2.5 Dynamic generalized linear models (DGLM)
63(3)
4.3 Multivariate Dynamic Linear Models
66(7)
4.3.1 Multivariate NDLMs
66(1)
4.3.2 Multivariate common-component NDLMs
66(1)
4.3.3 Matrix-variate NDLMs
67(1)
4.3.4 Hierarchical dynamic linear models (HDLM)
67(1)
4.3.5 Spatio-temporal models
68(5)
4.4 Further aspects of spatio-temporal modeling
73(8)
4.4.1 Process convolution based approaches
73(1)
4.4.2 Models based on stochastic partial differential equations
74(1)
4.4.3 Models based on integro-difference equations
75(6)
5 Geostatistical Modeling for Environmental Processes
81(16)
Sudipto Banerjee
5.1 Introduction
81(1)
5.2 Elements of point-referenced modeling
82(9)
5.2.1 Spatial processes, covariance functions, stationarity and isotropy
82(4)
5.2.2 Anisotropy and nonstationarity
86(1)
5.2.3 Variograms
87(4)
5.3 Spatial interpolation and kriging
91(3)
5.4 Summary
94(3)
6 Spatial and spatio-temporal point processes in ecological applications
97(36)
Janine B. Illian
6.1 Introduction - relevance of spatial point processes to ecology
98(2)
6.2 Point processes as mathematical objects
100(1)
6.3 Basic definitions
100(1)
6.4 Exploratory analysis - summary characteristics
101(4)
6.4.1 The Poisson process-a null model
101(1)
6.4.2 Descriptive methods
102(2)
6.4.3 Usage in ecology
104(1)
6.5 Point process models
105(6)
6.5.1 Modelling environmental heterogeneity - inhomogeneous Poisson processes and Cox processes
106(1)
6.5.2 Modelling clustering - Neyman Scott processes
107(2)
6.5.3 Modelling inter-individual interaction - Gibbs processes
109(1)
6.5.4 Model fitting - approaches and software
110(1)
6.5.4.1 Approaches
110(1)
6.5.4.2 Relevant software packages
111(1)
6.6 Point processes in ecological applications
111(1)
6.7 Marked point processes - complex data structures
112(4)
6.7.1 Different roles of marks in point patterns
113(1)
6.7.2 Complex models - dependence between marks and patterns
114(1)
6.7.3 Marked point pattern models reflecting the sampling process
115(1)
6.8 Modelling partially observed point patterns
116(4)
6.8.1 Point patterns observed in small subareas
117(2)
6.8.2 Distance sampling
119(1)
6.9 Discussion
120(5)
6.9.1 Spatial point processes and geo-referenced data
120(1)
6.9.2 Spatial point process modeling and statistical ecology
121(1)
6.9.3 Other data structures
122(1)
6.9.3.1 Telemetry data
122(1)
6.9.3.2 Spatio-temporal patterns
123(1)
6.9.4 Conclusion
124(1)
6.10 Acknowledgments
125(8)
7 Data assimilation
133(20)
Veronica J. Berrocal
7.1 Introduction
133(1)
7.2 Algorithms for data assimilation
134(7)
7.2.1 Optimal interpolation
136(1)
7.2.2 Variational approaches
137(2)
7.2.3 Sequential approaches: the Kalman filter
139(2)
7.3 Statistical approaches to data assimilation
141(12)
7.3.1 Joint modeling approaches
141(3)
7.3.2 Regression-based approaches
144(9)
8 Univariate and Multivariate Extremes for the Environmental Sciences
153(28)
Daniel Cooley
Brett D. Hunter
Richard L. Smith
8.1 Extremes and Environmental Studies
153(1)
8.2 Univariate Extremes
154(11)
8.2.1 Theoretical underpinnings
154(1)
8.2.2 Modeling Block Maxima
155(1)
8.2.3 Threshold exceedances
156(2)
8.2.4 Regression models for extremes
158(1)
8.2.5 Application: Fitting a time-varying GEV model to climate model output
159(1)
8.2.5.1 Analysis of individual ensembles and all data
160(1)
8.2.5.2 Borrowing strength across locations
161(4)
8.3 Multivariate Extremes
165(11)
8.3.1 Multivariate EVDs and componentwise block maxima
165(2)
8.3.2 Multivariate threshold exceedances
167(2)
8.3.3 Application: Santa Ana winds and dryness
169(1)
8.3.3.1 Assessing tail dependence
171(1)
8.3.3.2 Risk region occurrence probability estimation
174(2)
8.4 Conclusions
176(5)
9 Environmental Sampling Design
181(30)
Dale L. Zimmerman
Stephen T. Buckland
9.1 Introduction
181(1)
9.2 Sampling Design for Environmental Monitoring
182(16)
9.2.1 Design framework
182(1)
9.2.2 Model-based design
183(1)
9.2.2.1 Covariance estimation-based criteria
183(1)
9.2.2.2 Prediction-based criteria
184(1)
9.2.2.3 Mean estimation-based criteria
186(1)
9.2.2.4 Multi-objective and entropy-based criteria
187(1)
9.2.3 Probability-based spatial design
188(1)
9.2.3.1 Simple random sampling
188(1)
9.2.3.2 Systematic random sampling
189(1)
9.2.3.3 Stratified random sampling
189(1)
9.2.3.4 Variable probability sampling
190(1)
9.2.4 Space-filling designs
190(3)
9.2.5 Design for multivariate data and stream networks
193(2)
9.2.6 Space-time designs
195(3)
9.2.7 Discussion
198(1)
9.3 Sampling for Estimation of Abundance
198(14)
9.3.1 Distance sampling
199(1)
9.3.1.1 Standard probability-based designs
199(1)
9.3.1.2 Adaptive distance sampling designs
201(1)
9.3.1.3 Designed distance sampling experiments
203(2)
9.3.2 Capture-recapture
205(1)
9.3.2.1 Standard capture-recapture
205(1)
9.3.2.2 Spatial capture-recapture
205(1)
9.3.3 Discussion
206(5)
10 Accommodating so many zeros: univariate and multivariate data
211(30)
James S. Clark
Alan E. Gelfand
10.1 Introduction
212(3)
10.2 Basic univariate modeling ideas
215(6)
10.2.1 Zeros and ones
215(1)
10.2.2 Zero-inflated count data
216(1)
10.2.2.1 The k-ZIG
217(1)
10.2.2.2 Properties of the k-ZIG model
218(1)
10.2.2.3 Incorporating the covariates
219(1)
10.2.2.4 Model fitting and inference
219(1)
10.2.2.5 Hurdle models
220(1)
10.2.3 Zeros with continuous density G(y)
220(1)
10.3 Multinomial trials
221(3)
10.3.1 Ordinal categorical data
222(1)
10.3.2 Nominal categorical data
223(1)
10.4 Spatial and spatio-temporal versions
224(1)
10.5 Multivariate models with zeros
225(5)
10.5.1 Multivariate Gaussian models
226(1)
10.5.2 Joint species distribution models
227(1)
10.5.3 A general framework for zero-dominated multivariate data
227(1)
10.5.3.1 Model elements
228(1)
10.5.3.2 Specific data types
228(2)
10.6 Joint Attribute Modeling Application
230(4)
10.6.1 Host state and its microbiome composition
230(1)
10.6.2 Forest traits
230(4)
10.7 Summary and Challenges
234(7)
11 Gradient Analysis of Ecological Communities (Ordination)
241(34)
Michael W. Palmer
11.1 Introduction
242(1)
11.2 History of ordination methods
242(1)
11.3 Theory and background
243(6)
11.3.1 Properties of community data
243(1)
11.3.2 Coenospace
243(4)
11.3.3 Alpha, beta, gamma diversity
247(1)
11.3.4 Ecological similarity and distance
248(1)
11.4 Why ordination?
249(1)
11.5 Exploratory analysis and hypothesis testing
249(1)
11.6 Ordination vs. Factor Analysis
250(1)
11.7 A classification of ordination
251(1)
11.8 Informal techniques
251(1)
11.9 Distance-based techniques
251(4)
11.9.1 Polar ordination
252(1)
11.9.1.1 Interpretation of ordination scatter plots
253(1)
11.9.2 Principal coordinates analysis
254(1)
11.9.3 Nonmetric Multidimensional Scaling
254(1)
11.10 Eigenanalysis-based indirect gradient analysis
255(8)
11.10.1 Principal Components Analysis
256(2)
11.10.2 Correspondence Analysis
258(1)
11.10.3 Detrended Correspondence Analysis
259(3)
11.10.4 Contrast between DCA and NMDS
262(1)
11.11 Direct gradient analysis
263(7)
11.11.1 Canonical Correspondence Analysis
263(4)
11.11.2 Environmental variables in CCA
267(2)
11.11.3 Hypothesis testing
269(1)
11.11.4 Redundancy Analysis
269(1)
11.12 Extensions of direct ordination
270(1)
11.13 Conclusions
271(4)
II Topics in Ecological Processes 275(170)
12 Species distribution models
277(22)
Otso Ovaskainen
12.1 Aims of species distribution modelling
277(2)
12.2 Example data used in this chapter
279(1)
12.3 Single species distribution models
279(5)
12.4 Joint species distribution models
284(9)
12.4.1 Shared responses to environmental covariates
285(5)
12.4.2 Statistical co-occurrence
290(3)
12.5 Prior distributions
293(2)
12.6 Acknowledgments
295(4)
13 Capture-Recapture and distance sampling to estimate population sizes
299(22)
Richard J. Barker
13.1 Basic ideas
299(1)
13.2 Inference for closed populations
300(9)
13.2.1 Censuses and finite population sampling
301(1)
13.2.2 The problem of imperfect detection
301(1)
13.2.3 Capture-recapture on closed populations
302(2)
13.2.4 Distance sampling methods on closed populations
304(4)
13.2.5 N-mixture models for closed populations
308(1)
13.2.6 Count regression
309(1)
13.3 Inference for open populations
309(6)
13.3.1 Crosbie-Manly-Schwarz-Arnason model
310(1)
13.3.2 Cormack-Jolly-Seber model and tag-recovery models
311(2)
13.3.3 Pollock's robust design
313(1)
13.3.4 Capture recapture models for population growth rate
313(1)
13.3.5 Capture recapture models in terms of latent variable
314(1)
13.4 Combining observation and process models
315(1)
13.5 Software and model fitting
316(5)
14 Animal Movement Models
321(20)
Mevin Hooten
Devin Johnson
14.1 Introduction
321(1)
14.2 Data Models
322(2)
14.3 Point Process Models
324(2)
14.4 Discrete-Time Models
326(3)
14.5 Continuous-Time Models
329(6)
14.6 Conclusion
335(6)
15 Population Demography for Ecology
341(30)
Ken Newman
15.1 Introduction
342(2)
15.2 Components of demography
344(3)
15.2.1 Multiple subpopulations
344(1)
15.2.2 Multiple processes
345(1)
15.2.3 Stochasticity
345(1)
15.2.4 Density dependence
346(1)
15.2.5 Competitors, predators, and prey
346(1)
15.2.6 Human manipulation of dynamics
346(1)
15.2.7 Uncertainty in abundances
346(1)
15.3 General mathematical features of PDMs
347(4)
15.3.1 Multiple subpopulations
347(1)
15.3.2 Multiple processes
347(2)
15.3.3 Stochasticity
349(1)
15.3.4 Density dependence
350(1)
15.3.5 Inclusion of covariates
351(1)
15.3.6 Remarks: Estimability and Data Collection.
351(1)
15.4 Matrix Projection Models, MPMs
351(4)
15.4.1 Analysis of MPMs
352(1)
15.4.2 Limiting behavior of density independent, time invariate MPMs
352(1)
15.4.3 Stochasticity
353(1)
15.4.4 Building block approach to matrix construction
354(1)
15.4.5 Determining the elements of projection matrices
355(1)
15.4.6 Density dependent MPMs
355(1)
15.5 Integral Projection Models, IPMs
355(3)
15.5.1 Kernel structure of IPMs.
356(1)
15.5.2 Implementation of an IPM
357(1)
15.5.3 Estimation of kernel components
357(1)
15.5.4 Application, use and analysis of IPMs
358(1)
15.6 Individual Based Models, IBMs
358(3)
15.6.1 Statistical designs for and analysis of IBMs
359(1)
15.6.2 Comparison with population models
359(1)
15.6.3 Applications of IBMs
360(1)
15.6.4 Data needs and structure
360(1)
15.6.5 Relationship with IPMs
361(1)
15.7 State-Space Models, SSMs
361(2)
15.7.1 Normal dynamic linear models
362(1)
15.7.2 Non-normal, nonlinear SSMs
362(1)
15.7.3 Hierarchical and continuous time SSMs
363(1)
15.8 Concluding Remarks
363(8)
15.8.1 Omissions and sparse coverage
363(1)
15.8.2 Recommended literature
364(1)
15.8.3 Speculations on future developments
364(7)
16 Statistical Methods for Modeling Traits
371(30)
Matthew Aiello-Lammens
John A. Silander Jr
16.1 Introduction
371(3)
16.1.1 What Are We Modeling?
373(1)
16.1.2 Traits Versus "Functional Traits"
373(1)
16.2 Overview of Data for Trait Modeling
374(2)
16.2.1 Example data sets
375(1)
16.3 Exploratory Data Analysis
376(2)
16.3.1 Dimension Reduction of Trait Data
376(2)
16.4 Trait Modeling - Algorithmic
378(13)
16.4.1 Redundancy Analysis on Individual-Level Trait Data
379(3)
16.4.2 Community Aggregated Trait Metrics
382(1)
16.4.2.1 CWM-RDA
382(1)
16.4.2.2 CWM Randomization Approaches
383(1)
16.4.2.3 Concerns with CWM approaches
385(1)
16.4.3 Fourth-corner Methods
386(1)
16.4.3.1 Fourth-corner Problem
386(1)
16.4.3.2 RLQ Analysis
388(1)
16.4.3.3 Maximum Entropy
391(1)
16.5 Trait Modeling - Statistical Model-Based
391(1)
16.6 Conclusion
392(1)
16.7 Acknowledgments
393(8)
17 Statistical models of vegetation fires: Spatial and temporal patterns
401(20)
J.M.C. Pereira
K.F. Turkman
17.1 Introduction
401(5)
17.1.1 The global relevance of vegetation fires
401(1)
17.1.2 Fire likelihood, intensity, and effects
402(1)
17.1.3 Acquisition of fire data from Earth observation satellites
403(2)
17.1.4 Research overview
405(1)
17.2 Statistical methods and models for vegetation fire studies
406(15)
17.2.1 Spatio-temporal point patterns of vegetation fires
407(1)
17.2.2 Models for fire sizes
408(1)
17.2.3 Models for fire incidence and fire frequency data
409(2)
17.2.4 Measures of risk for vegetation fires and fire risk maps
411(1)
17.2.5 Post-fire vegetation recovery
412(1)
17.2.6 Weekly cycles of vegetation burning as anthropogenic fingerprint
413(8)
18 Spatial Statistical Models for Stream Networks
421(24)
Jay M. Ver Hoef
Erin E. Peterson
Daniel J. Isaak
18.1 Introduction
421(7)
18.1.1 Motivating Example
422(3)
18.1.2 Why Stream Network Models?
425(3)
18.2 Preliminaries
428(3)
18.2.1 Notation
428(2)
18.2.2 Computing Distance in a Branching Network
430(1)
18.3 Moving Average Construction for Spatial Error Process
431(5)
18.3.1 Tail-up models
432(2)
18.3.2 Tail-down models
434(1)
18.3.3 Spatial Linear Mixed Models
435(1)
18.4 Example
436(4)
18.4.1 Estimation
436(1)
18.4.2 Torgegram
437(1)
18.4.3 Prediction
438(2)
18.4.4 Software
440(1)
18.5 Summary
440(5)
III Topics in Environmental Exposure 445(172)
19 Statistical methods for exposure assessment
447(18)
Montse Fuentes
Brian J. Reich
Yen-Ning Huang
19.1 Defining Exposure
447(2)
19.2 Spatiotemporal Mapping of Monitoring Data
449(6)
19.2.1 K-Nearest Neighbor (KNN) interpolation
449(1)
19.2.2 Inverse Distance Weighting (IDW)
450(1)
19.2.3 Kriging
450(2)
19.2.4 Bayesian Interpolation
452(1)
19.2.5 Comparison of methods
453(1)
19.2.6 Case study: PM2.5 data in the Eastern US
453(2)
19.3 Spatiotemporal extensions
455(3)
19.4 Data Fusion
458(7)
19.4.1 Calibration of Computer Models
458(1)
19.4.2 Spatial Downscaler
459(1)
19.4.3 Spatial Bayesian Melding
459(1)
19.4.4 Case Study: Statistical downscale of PM2.5
460(5)
20 Alternative models for estimating air pollution exposures - Land Use Regression and Stochastic Human Exposure and Dose Simulation for particulate matter (SHEDS-PM)
465(20)
Joshua L. Warren
Michelle L. Bell
20.1 Introduction
465(1)
20.2 Land Use Regression Modeling
466(6)
20.2.1 Background
466(1)
20.2.2 Land Use Regression Methods
467(3)
20.2.3 Examples of Land Use Regression
470(1)
20.2.4 Limitations to Land Use Regression
471(1)
20.3 Population Exposure Modeling
472(6)
20.3.1 Background
472(1)
20.3.2 Stochastic Human Exposure and Dose Simulation for particulate matter (SHEDS-PM)
473(3)
20.3.3 Examples of SHEDS-PM Use
476(1)
20.3.4 Limitations to SHEDS-PM
477(1)
20.4 Conclusions
478(7)
21 Preferential sampling of exposure levels
485(14)
Peter J. Diggle
Emanuele Giorgi
21.1 Introduction
485(1)
21.2 Geostatistical sampling designs
486(1)
21.2.1 Definitions
486(1)
21.3 Preferential sampling methodology
487(5)
21.3.1 Non-uniform designs need not be preferential
488(1)
21.3.2 Adaptive designs need not be strongly preferential
488(1)
21.3.3 The Diggle, Menezes and Su model
489(1)
21.3.4 The Pati, Reich and Dunson model
489(1)
21.3.4.1 Monte Carlo maximum likelihood using stochastic partial differential equations
490(2)
21.4 Application: lead pollution monitoring
492(2)
21.5 Discussion
494(5)
22 Monitoring network design
499(24)
James V. Zidek
Dale L. Zimmerman
22.1 Introduction
499(2)
22.2 Monitoring environmental processes
501(1)
22.3 Design objectives
502(1)
22.4 Design paradigms
503(1)
22.5 Probability-based designs
504(2)
22.6 Model based designs
506(9)
22.6.1 Estimation of covariance parameters
506(2)
22.6.2 Estimation of mean parameters: The regression model approach
508(1)
22.6.3 Spatial prediction
509(1)
22.6.4 Prediction and process model inference
510(1)
22.6.5 Entropy-based design
511(4)
22.7 From ambient monitors to personal exposures
515(1)
22.8 New directions
516(1)
22.9 Concluding remarks
517(6)
23 Statistical methods for source apportionment
523(24)
Jenna R. Krall
Howard H. Chang
23.1 Introduction
523(2)
23.1.1 Source apportionment
524(1)
23.1.2 Example
525(1)
23.2 Methods when source profiles are known
525(3)
23.2.1 Ordinary least squares approaches
527(1)
23.2.2 Chemical Mass Balance (CMB)
527(1)
23.3 Methods when source profiles are unknown
528(5)
23.3.1 Principal component analysis (PCA)
528(1)
23.3.2 Absolute principal component analysis (APCA)
529(1)
23.3.3 Unmix
529(1)
23.3.4 Factor analytic methods
530(1)
23.3.5 Positive matrix factorization
530(1)
23.3.6 Bayesian approaches
531(1)
23.3.7 Ensemble approaches
532(1)
23.4 Comparison of source apportionment methods
533(1)
23.5 Challenges in source apportionment
534(6)
23.5.1 Number of sources
535(2)
23.5.2 Incorporating uncertainty
537(1)
23.5.3 Measurement error
538(1)
23.5.4 Temporal variation
538(1)
23.5.5 Evaluation of source apportionment results
539(1)
23.5.6 Multiple site data
539(1)
23.6 Estimating source-specific health effects
540(1)
23.7 Conclusions
541(6)
24 Statistical Methods for Environmental Epidemiology
547(40)
Francesca Dominici
Ander Wilson
24.1 Introduction
547(3)
24.1.1 Data Characteristics
548(1)
24.1.2 Sources of Confounding Bias
549(1)
24.2 Epidemiological Designs
550(9)
24.2.1 Multi-Site Time Series Studies
551(1)
24.2.1.1 Distributed Lag Models
552(1)
24.2.2 Cohort Studies
553(1)
24.2.3 Intervention Studies
554(2)
24.2.4 Spatial Misalignment
556(2)
24.2.5 Exposure Prediction Modeling
558(1)
24.3 Estimating the Exposure-Response Relationship
559(2)
24.3.1 Generalized Linear Models
559(1)
24.3.2 Semi-Parametric Approaches
560(1)
24.3.3 Model Uncertainty in the Shape of the Exposure-Response
560(1)
24.4 Confounding Adjustment
561(6)
24.4.1 Bayesian Adjustment for Confounding
562(2)
24.4.2 Relation to BMA
564(1)
24.4.3 Air Pollution Example
564(1)
24.4.4 Concluding Remarks
565(2)
24.5 Estimation of Health Effects From Simultaneous Exposure to Multiple Pollutants
567(20)
24.5.1 Multi-Pollutant Profile Clustering and Effect Estimation
568(1)
24.5.2 High-Dimensional Exposure-Response Function Estimation
569(1)
24.5.3 Confounding Adjustment in Multiple Pollutant Models
569(18)
25 Connecting Exposure to Outcome: Exposure Assessment
587(16)
Adam A. Szpiro
25.1 Background and overview of this chapter
587(2)
25.2 Spatial statistics for exposure assessment
589(4)
25.2.1 Land-Use Regression and Universal Kriging
589(1)
25.2.2 Example 1: Stepwise Variable Selection in LUR
590(1)
25.2.3 Example 2: Distance Decay Variable Selection (ADDRESS) in LUR
591(1)
25.2.4 Example 3: Lasso Followed by Exhaustive Search Variable Selection in LUR and UK
591(1)
25.2.5 Example 4: Accurate exposure prediction does not necessarily improve health effect estimation
592(1)
25.3 Measurement error for spatially misaligned data
593(5)
25.3.1 Correctly specified LUR or UK exposure model
593(2)
25.3.2 Incorrectly specified LUR or regression spline exposure model
595(3)
25.4 Optimizing exposure modeling for health effect estimation rather than prediction accuracy
598(5)
26 Environmental epidemiology study designs
603(14)
Lianne Sheppard
26.1 Introduction
603(2)
26.2 Studies that focus on short-term variation of exposures and acute effects
605(5)
26.2.1 Ecologic time series studies
605(1)
26.2.2 Case-crossover studies
606(3)
26.2.3 Panel studies
609(1)
26.3 Studies that focus on long-term average exposures and chronic health effects
610(2)
26.3.1 Cohort studies
610(1)
26.3.2 Case-control and cross-sectional studies
611(1)
26.4 Summary and Discussion
612(5)
IV Topics in Climatology 617(224)
27 Modeling and assessing climatic trends
619(22)
Peter F. Craigmile
Peter Guttorp
27.1 Introduction
619(1)
27.2 Two motivating examples
620(1)
27.2.1 US average temperature anomaly
620(1)
27.2.2 Global temperature series
621(1)
27.3 Time series approaches
621(7)
27.3.1 Candidate models for the noise
622(1)
27.3.2 Linear trends
623(2)
27.3.3 Nonlinear and nonparametric trends
625(2)
27.3.4 Smoothing and filtering to estimate the trend
627(1)
27.3.5 Removing or simplifying trend by differencing
627(1)
27.3.6 Hierarchical and dynamic linear model decompositions for trend
628(1)
27.4 Two case studies
628(4)
27.4.1 US annual temperatures
628(2)
27.4.2 Global annual mean temperature
630(2)
27.5 Spatial and spatio-temporal trends
632(1)
27.6 Assessing climatic trends in other contexts
633(1)
27.7 Discussion
633(8)
28 Climate Modelling
641(16)
David B. Stephenson
28.1 Aim
641(1)
28.2 What is climate?
642(1)
28.3 Climate modelling
643(3)
28.3.1 Climate processes
643(1)
28.3.2 Classes of climate model
644(1)
28.3.2.1 General Circulation Model (GCM)
644(1)
28.3.2.2 Regional Climate Model (RCM)
645(1)
28.3.2.3 Earth System Model (ESM)
645(1)
28.3.2.4 Low-order models
645(1)
28.3.2.5 Stochastic Climate Models
646(1)
28.4 Design of Experiments for Climate Change
646(4)
28.4.1 Initial condition ensembles (ICE)
647(1)
28.4.2 Perturbed Physics Ensembles (PPE)
647(1)
28.4.3 Multi-Model Ensembles (MME)
647(2)
28.4.4 Climate change projections
649(1)
28.5 Real world inference from climate model data
650(3)
28.5.1 Current practice
650(1)
28.5.2 Imperfect climate model and observational data
650(2)
28.5.3 Probabilistic inference
652(1)
28.5.3.1 The truth-centered approach
652(1)
28.5.3.2 The coexchangeable approach
652(1)
28.5.4 Summary
652(1)
28.6 Concluding remarks
653(4)
29 Spatial Analysis in Climatology
657(30)
Douglas Nychka
Christopher K. Wikle
29.1 Introduction
657(1)
29.2 Exploratory/Descriptive Analysis
658(10)
29.2.1 Moment-Based Methods
658(1)
29.2.2 Spectral-Based Methods
659(3)
29.2.3 Eigen-Decomposition-Based Methods
662(1)
29.2.3.1 Empirical Orthogonal Functions (EOFs)
662(1)
29.2.3.2 Spatio-Temporal Canonical Correlation Analysis (ST-CCA)
667(1)
29.2.3.3 Empirical Principal Oscillation Patterns (POPs)/Empirical Normal Modes (ENMs)
667(1)
29.3 Data Products
668(10)
29.3.1 Data Assimilation
668(3)
29.3.2 Spatial Prediction
671(3)
29.3.3 Inference for spatial fields
674(1)
29.3.3.1 Spatial and Spatio-Temporal Field Comparison
676(2)
29.3.4 Spatio-Temporal Prediction
678(1)
29.4 Conclusion
678(1)
29.5 Acknowledgments
679(1)
29.6 Figures
679(8)
30 Assimilating Data into Models
687(24)
Amarjit Budhiraja
Eric Friedlander
Cohn Guider
Christopher K.R.T. Jones
John Maclean
30.1 Introduction
688(6)
30.1.1 The core of a DA scheme
689(1)
30.1.2 Model and observations
689(1)
30.1.3 Challenges of DA
690(1)
30.1.4 Approaches to DA
691(1)
30.1.4.1 Variational approach
691(1)
30.1.4.2 Kalman gain approach
691(1)
30.1.4.3 Probabilistic approach
692(1)
30.1.5 Perspectives on DA
693(1)
30.1.6
Chapter Overview
694(1)
30.2 Variational Methods
694(5)
30.2.1 3D-Var
695(1)
30.2.1.1 Incremental Method for 3D-Var
695(1)
30.2.2 4D-Var
696(1)
30.2.2.1 Strong constraint 4D-Var
696(1)
30.2.2.2 Incremental Method for 4D-Var
697(1)
30.2.2.3 Weak Constraint 4D-Var
698(1)
30.3 Bayesian formulation and sequential methods
699(6)
30.3.1 Filtering
699(1)
30.3.2 The Kalman Filter
700(1)
30.3.2.1 Extensions
701(1)
30.3.2.2 Equivalence of 4D-Var and KF
702(1)
30.3.3 Particle Filters
703(1)
30.3.3.1 A basic particle filter
703(1)
30.3.3.2 Particle filter with resampling
704(1)
30.3.3.3 Variance reduction: Deterministic allocation and residual resampling
704(1)
30.3.3.4 Branching particle filter
704(1)
30.3.3.5 Regularized particle filters
705(1)
30.4 Implementation of DA methods
705(6)
30.4.1 Common modifications for DA schemes
707(1)
30.4.1.1 Localization
707(1)
30.4.1.2 Inflation
707(4)
31 Spatial Extremes
711(34)
Anthony Davison
Raphael Huser
Emeric Thibaud
31.1 Introduction
711(2)
31.2 Max-stable and related processes
713(6)
31.2.1 Poisson process
713(2)
31.2.2 Classical results
715(1)
31.2.3 Spectral representation
716(3)
31.2.4 Exceedances
719(1)
31.3 Models
719(4)
31.3.1 General
719(1)
31.3.2 Brown-Resnick process
720(1)
31.3.3 Extremal-t process
721(1)
31.3.4 Other models
721(1)
31.3.5 Asymptotic independence
722(1)
31.4 Exploratory procedures
723(1)
31.5 Inference
724(3)
31.5.1 General
724(1)
31.5.2 Likelihood inference for maxima
725(1)
31.5.3 Likelihood inference for threshold exceedances
726(1)
31.6 Examples
727(10)
31.6.1 Saudi Arabian rainfall
727(7)
31.6.2 Spanish temperatures
734(3)
31.7 Discussion
737(1)
31.8 Computing
738(7)
32 Statistics in Oceanography
745(22)
Christopher K. Wikle
32.1 Introduction
745(1)
32.2 Descriptive Multivariate Methods
746(1)
32.2.1 PCA and EOF Analysis
746(1)
32.2.2 Spatio-Temporal Canonical Correlation Analysis (ST-CCA)
747(1)
32.3 Time Series Methods
747(6)
32.3.1 Time-Domain Methods
748(1)
32.3.2 Frequency-Domain Methods
748(1)
32.3.2.1 Univariate Spectral Analysis
749(1)
32.3.2.2 Bivariate Spectral Analysis
750(1)
32.3.2.3 Space-Time Spectral Analysis
753(1)
32.4 Spatio-Temporal Methods
753(2)
32.5 Methods for Data Assimilation
755(2)
32.5.1 Assimilating Near Surface Ocean Winds
755(1)
32.5.2 Assimilating Lower Trophic Ecosystem Components
756(1)
32.6 Methods for Long-Lead Forecasting
757(4)
32.6.1 Multivariate Methods
757(1)
32.6.2 Autoregressive and State-Space Approaches
757(1)
32.6.3 Alternative Approaches
758(1)
32.6.4 Long-Lead Forecast Example: Pacific SST
758(1)
32.6.4.1 SST Forecast Model
759(1)
32.6.4.2 Results
759(2)
32.7 Conclusion
761(1)
32.8 Acknowledgments
761(6)
33 Paleoclimate reconstruction: looking backwards to look forward
767(22)
Peter F. Craigmile
Murali Haran
Bo Li
Elizabeth Mannshardt
Bala Rajaratnam
Martin Tingley
33.1 Introduction
768(1)
33.2 Paleoclimate reconstruction: looking backwards
769(7)
33.2.1 A multiproxy, multiforcing IR reconstruction
770(1)
33.2.2 Statistical issues in paleoclimate reconstruction
771(1)
33.2.2.1 Incorporating climate forcings in the HBM
771(1)
33.2.2.2 Handling proxies separately
772(1)
33.2.2.3 Modeling temporal dependence
772(1)
33.2.2.4 Modeling spatial dependence and spatio-temporal reconstructions
773(1)
33.2.2.5 Missing values and data augmentation
774(1)
33.2.2.6 Temporal uncertainty
774(1)
33.2.2.7 Non-Gaussian paleoclimate reconstruction
774(1)
33.2.2.8 Multivariate reconstructions
775(1)
33.2.3 Ideas and good practices
775(1)
33.3 Climate models and paleoclimate
776(4)
33.3.1 Climate model assessment using paleoclimate reconstructions
776(2)
33.3.2 Statistical issues
778(1)
33.3.2.1 Considering and embracing the lack of independence
778(1)
33.3.2.2 Refining model components
778(1)
33.3.3 Research directions
779(1)
33.3.3.1 Paleoclimate-based climate model calibration
779(1)
33.3.3.2 Making climate projections using paleoclimate reconstructions
779(1)
33.3.3.3 Paleoclimate reconstructions using climate models
779(1)
33.4 Discussion: looking forward
780(9)
34 Climate Change Detection and Attribution
789(30)
Dorit Hammerling
Matthias Katzfuss
Richard Smith
34.1 Introduction
789(2)
34.2 Statistical model description
791(1)
34.3 Methodological development
792(7)
34.3.1 The beginning: Hasselmann's method and its enhancements
792(2)
34.3.2 The method comes to maturity: Reformulation as a regression problem; random effects and total least squares
794(1)
34.3.3 Accounting for noise in model-simulated responses: the total least squares algorithm
795(2)
34.3.4 Combining multiple climate models
797(1)
34.3.5 Recent advances
798(1)
34.4 Attribution of extreme events
799(13)
34.4.1 Introduction
799(1)
34.4.2 Framing the question
800(2)
34.4.3 Other "Framing" Issues
802(3)
34.4.4 Statistical methods
805(1)
34.4.5 Application to precipitation data from Hurricane Harvey
806(2)
34.4.6 An example
808(4)
34.4.7 Another approach
812(1)
34.5 Summary and open questions
812(1)
34.6 Acknowledgments
813(6)
35 Health risks of climate variability and change
819(22)
Kristie L. Ebi
David Hondula
Patrick Kinney
Andrew Monaghan
Cory W. Morin
Nick Ogden
Marco Springmann
35.1 Introduction
820(1)
35.2 Framework of the health risks of climate variability and change
821(1)
35.3 Quantifying the associations between weather/climate and health
821(7)
35.3.1 Cases of adverse health outcomes
822(1)
35.3.2 Human sensitivity to disease risk
823(1)
35.3.3 Exposure risk
823(1)
35.3.4 Analyzing associations between exposures to weather/climate variability and adverse health outcomes
823(1)
35.3.5 Spatial analyses
824(1)
35.3.6 Vulnerability mapping
825(1)
35.3.7 Cautions and considerations
826(2)
35.4 Modeling future risks of climate-sensitive health outcomes
828(6)
35.4.1 Spatiotemporal issues and other considerations when using climate projections
829(2)
35.4.2 Projections using statistical models
831(1)
35.4.3 Projections using process-based models
832(1)
35.4.4 Other considerations
832(1)
35.4.5 Scenarios
833(1)
35.5 Conclusions
834(7)
Index 841
Alan E. Gelfand is the James B. Duke Professor of Statistical Science at Duke University. He is a leader in Bayesian spatial modeling and analysis including a successful book in this area with Banerjee and Carlin.

Montserrat (Montse) Fuentes, Ph.D., became dean of the Virginia Commonwealth University College of Humanities and Sciences on July 1, 2016. She came to VCU from North Carolina State University, where she served as the head of the Department of Statistics and James M. Goodnight Distinguished Professor of Statistics. She also served as center director for the Research Network for Statistical Methods for Atmospheric and Oceanic Sciences, a research collaborative funded by the National Science Foundation. She received a dual bachelors degree in mathematics and music (piano) from the University of Valladolid in Spain and a Ph.D. in statistics from the University of Chicago.

Jennifer A. Hoeting is a Professor of Statistics at Colorado State University, where she has worked since 1994. She received her PhD from the University of Washington.

Richard L. Smith is Mark L. Reed III Distinguished Professor of Statistics and Professor of Biostatistics in the University of North Carolina, Chapel Hill. From 2010-2017 he was also Director of the Statistical and Applied Mathematical Sciences Institute, a Mathematical Sciences Institute supported by the National Science Foundation, and he will continue (through June 2018) as Associate Director of SAMSI. He obtained his PhD from Cornell University and previously held academic positions at Imperial College (London), the University of Surrey (Guildford, England) and Cambridge University. His main research interest is environmental statistics and associated areas of methodological research such as spatial statistics, time series analysis and extreme value theory. He is particularly interested in statistical aspects of climate change research, and in air pollution including its health effects. He is a Fellow of the American Statistical Association and the Institute of Mathematical Statistics, an Elected Member of the International Statistical Institute, and has won the Guy Medal in Silver of the Royal Statistical Society, and the Distinguished Achievement Medal of the Section on Statistics and the Environment, American Statistical Association. In 2004 he was the J. Stuart Hunter Lecturer of The International Environmetrics Society (TIES). He is also a Chartered Statistician of the Royal Statistical Society.
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