Statistical Analysis of Environmental Space-time Processes

by Le, Nhu D.; Zidek, James V.

• ISBN13: 9780387262093
• ISBN10: 0387262091
• Format: Hardcover
• Copyright: 2006-05-30
• Publisher: Springer Verlag

Summary

This book provides a broad introduction to the fascinating subject of environmental space-time processes; addressing the role of uncertainty. Within that context, it covers a spectrum of technical matters from measurement to environmental epidemiology to risk assessment. It showcases non-stationary vector-valued processes, while treating stationarity as a special case. The contents reflect the authors' cumulative knowledge gained over many years of consulting and research collaboration. In particular, with members of their research group, they developed within a hierarchical Bayesian framework, the new statistical approaches presented in the book for analyzing, modeling, and monitoring environmental spatio-temporal processes. Furthermore they indicate new directions for development.This book contains technical and non-technical material and it is written for statistical scientists as well as consultants, subject area researchers and students in related fields. Novel chapters present the authors' hierarchical Bayesian approaches to:- spatially interpolating environmental processes- designing networks to monitor environmental processes- multivariate extreme value theory- incorporating risk assessmentIn addition, they present a comprehensive and critical survey of other approaches, highlighting deficiencies that their method seeks to overcome. Special sections marked by an asterisk provide rigorous development for readers with a strong technical background. Alternatively readers can go straight to the tutorials supplied in chapter 14 and learn how to apply the free, downloadable modeling and design software that the authors and their research partners have developed.

Author Biography

Jim Zidek is a Professor Emeritus and Founding Head of the Department of Statistics at the University of British Columbia. Nhu Le is a Senior Scientist in Cancer Control Research and a former Director of the Occupational Oncology Research Program at the British Columbia Cancer Agency (BCCA). He is also an Adjunct Professor of Statistics at the University of British Columbia.

Table of Contents

Preface
Part I: Environmental Processes
1 First Encounters	3	(12)
1.1 Environmental Fields	3	(7)
1.1.1 Examples	8	(2)
1.2 Modeling Foundations	10	(3)
1.2.1 Space-Time Domains	11	(1)
1.2.2 Procedure Performance Paradigms	11	(1)
1.2.3 Bayesian Paradigm	12	(1)
1.2.4 Space-time Fields	13	(1)
1.3 Wrapup	13	(2)
2 Case Study	15	(12)
2.1 The Data	15	(1)
2.2 Preliminaries	16	(3)
2.3 Space--time Process Modeling	19	(1)
2.4 Results!	19	(5)
2.5 Wrapup	24	(3)
3 Uncertainty	27	(8)
3.1 Probability: "The Language of Uncertainty"	27	(1)
3.2 Probability and Uncertainty	28	(2)
3.3 Uncertainty Versus Information	30	(3)
3.3.1 Variance	31	(1)
3.3.2 Entropy	32	(1)
3.4 Wrapup	33	(2)
4 Measurement	35	(18)
4.1 Spatial Sampling	36	(6)
4.1.1 Acid Precipitation	36	(3)
4.1.2 The Problem of Design Objectives	39	(1)
4.1.3 A Probability-Based Design Solution	40	(1)
4.1.4 Pervasive Principles	41	(1)
4.2 Sampling Techniques	42	(3)
4.2.1 Measurement: The Illusion!	42	(1)
4.2.2 Air Pollution	42	(1)
4.2.3 Acid Precipitation Again	43	(1)
4.2.4 Toxicology and Biomarkers	44	(1)
4.3 Data Quality	45	(1)
4.3.1 Cost Versus Precision	45	(1)
4.3.2 Interlaboratory and Measurement Issues	45	(1)
4.4 Measurement Error	46	(3)
4.4.1 A Taxonomy of Types	47	(2)
4.5 Effects	49	(2)
4.5.1 Subtleties	50	(1)
4.6 Wrapup	51	(2)
5 Modeling	53	(30)
5.1 Why Model?	53	(3)
5.2 What Makes a Model Good?	56	(1)
5.3 Approaches to Modeling***	57	(17)
5.3.1 Modeling with Marginals	59	(1)
5.3.2 Modeling by Conditioning	59	(1)
5.3.3 Single Timepoints	60	(1)
5.3.4 Hierarchical Bayesian Modeling	61	(1)
5.3.5 Dynamic state-space Models	62	(1)
5.3.6 Orthogonal Series	63	(3)
5.3.7 Computer Graphical Models	66	(2)
5.3.8 Markov Random Fields	68	(2)
5.3.9 Latent Variable Methods	70	(1)
5.3.10 Physical-Statistical Models	71	(3)
5.4 Gaussian Fields	74	(3)
5.5 Log Gaussian Processes	77	(1)
5.6 Wrapup	78	(5)
Part II: Space—Time Modeling
6 Covariances	83	(18)
6.1 Moments and Variograms	84	(2)
6.1.1 Finite-Dimensional Distributions	84	(2)
6.2 Stationarity	86	(2)
6.3 Variogram Models for Stationary Processes	88	(1)
6.3.1 Characteristics of Covariance Functions	88	(1)
6.4 Isotropic Semi-Variogram Models	89	(4)
6.5 Correlation Models for Nonstationary Processes	93	(6)
6.5.1 The Sampson–Guttorp Method	93	(4)
6.5.2 The Higdon, Swall, and Kern Method	97	(1)
6.5.3 The Fuentes Method	98	(1)
6.6 Wrapup	99	(2)
7 Spatial Prediction: Classical Approaches	101	(18)
7.1 Ordinary Kriging	104	(3)
7.2 Universal Kriging	107	(4)
7.3 Cokriging	111	(2)
7.4 Disjunctive Kriging	113	(3)
7.5 Wrapup	116	(3)
8 Bayesian Kriging	119	(12)
8.1 The Kitanidis Framework***	121	(3)
8.1.1 Model Specification	121	(1)
8.1.2 Prior Distribution	122	(1)
8.1.3 Predictive Distribution	123	(1)
8.1.4 Remarks	123	(1)
8.2 The Handcock and Stein Method***	124	(2)
8.3 The Bayesian Transformed Gaussian Approach	126	(4)
8.3.1 The BTG Model	127	(1)
8.3.2 Prior Distribution	128	(1)
8.3.3 Predictive Distribution	128	(1)
8.3.4 Numerical Integration Algorithm	129	(1)
8.4 Remarks	130	(1)
9 Hierarchical Bayesian Kriging	131
9.1 Univariate Setting	134	(7)
9.1.1 Model Specification	135	(1)
9.1.2 Predictive Distribution	136	(5)
9.2 Missing Data	141	(1)
9.3 Staircase Pattern of Missing Data	142	(6)
9.3.1 Notation	143	(2)
9.3.2 Staircase Model Specification	145	(1)
9.3.3 The GIW Distribution	146	(1)
9.3.4 Predictive Distributions	146	(2)
9.4 Wrapup	148	(5)
Part III: Design and Risk Assessment
10 Multivariate Modeling***	153	(32)
10.1 General Staircase	155	(3)
10.1.1 Notation	155	(3)
10.2 Model Specification	158	(1)
10.3 Predictive Distributions	159	(3)
10.4 Posterior Distributions	162	(3)
10.5 Posterior Expectations	165	(2)
10.6 Hyperparameter Estimation	167	(11)
10.6.1 Two-Step Estimation Procedure	167	(1)
10.6.2 Spatial Covariance Separability	168	(3)
10.6.3 Estimating Gauged Site Hyperparameters	171	(6)
10.6.4 Estimating Ungauged Site Hyperparameters	177	(1)
10.7 Systematically Missing Data	178	(3)
10.8 Credibility Ellipsoids	181	(2)
10.9 Wrapup	183	(2)
11 Environmental Network Design	185	(30)
11.1 Design Strategies	187	(4)
11.2 Entropy-Based Designs	191	(1)
11.3 Entropy	191	(3)
11.4 Entropy in Environmental Network Design	194	(2)
11.5 Entropy Criteria	196	(1)
11.6 Predictive Distribution	196	(2)
11.7 Criteria	198	(1)
11.8 Incorporating Cost	199	(1)
11.9 Computation***	200	(2)
11.10 Case Study	202	(4)
11.11 Pervasive Issues***	206	(7)
11.12 Wrapup	213	(2)
12 Extremes	215	(30)
12.1 Fields of Extremes	216	(4)
12.1.1 Theory of Extremes	216	(4)
12.2 Hierarchical Bayesian Model	220	(2)
12.2.1 Empirical Assessment	221	(1)
12.3 Designer Challenges	222	(17)
12.3.1 Loss of Spatial Dependence	222	(5)
12.3.2 Uncertain Design Objectives	227	(12)
12.4 Entropy Designs for Monitoring Extremes	239	(2)
12.5 Wrapup	241	(4)
Part IV: Implementation
13 Risk Assessment	245	(26)
13.1 Environmental Risk Model	245	(1)
13.2 Environmental Risk	246	(3)
13.3 Risk in Postnormal Science	249	(3)
13.4 Environmental Epidemiology***	252	(11)
13.4.1 Impact Assessment***	253	(10)
13.5 Case Study	263	(5)
13.6 Wrapup	268	(3)
14 R Tutorial	271	(26)
14.1 Exploratory Analysis of the Data	272	(6)
14.2 Spatial Predictive Distribution and Parameter Estimation	278	(12)
14.2.1 Parameter Estimation: Gauged Sites Through the EM-algorithm	279	(3)
14.2.2 Parameter Estimation: The Sampson–Guttorp Method	282	(8)
14.2.3 Parameter Estimation: Ungauged Sites	290	(1)
14.3 Spatial Interpolation	290	(1)
14.4 Monitoring Network Extension	291	(6)
Appendices	297	(16)
15.1 Probabilistic Distributions	297	(5)
15.1.1 Multivariate and Matrix Normal Distribution	297	(1)
15.1.2 Multivariate and Matric-t Distribution	298	(1)
15.1.3 Wishart and Inverted Wishart Distribution	299	(1)
15.1.4 Generalized Inverted Wishart Distribution	300	(2)
15.2 Bartlett Decomposition	302	(1)
15.2.1 Two-Block Decomposition	302	(1)
15.2.2 Recursive Bartlett Decomposition for Multiple Blocks	302	(1)
15.3 Useful Matrix Properties	303	(4)
15.4 Proofs for Chapter 10	307	(6)
References	313	(14)
Author Index	327	(4)
Subject Index	331