Teaches Students How to Perform Spatio-Temporal Analyses within Epidemiological StudiesSpatio-Temporal Methods in Environmental Epidemiology is the first book of its kind to specifically address the interface between environmental epidemiology and spatio-temporal modeling. In response to the growing need for collaboration between statisticians and

Spatio-Temporal Methods in Environmental Epidemiology with R, like its First Edition, explores the interface between environmental epidemiology and spatio-temporal modeling. It links recent developments in spatio-temporal theory with epidemiological applications. Drawing on real-life problems, it shows how recent advances in methodology can assess the health risks associated with environmental hazards. The book's clear guidelines enable the implementation of the methodology and estimation of risks in practice. New additions to the Second Edition include: a thorough exploration of the underlying concepts behind knowledge discovery through data; a new chapter on extracting information from data using R and the tidyverse; additional material on methods for Bayesian computation, including the use of NIMBLE and Stan; new methods for performing spatio-temporal analysis and an updated chapter containing further topics. Throughout the book there are new examples, and the presentation of R code for examples has been extended. Along with these additions, the book now has a GitHub site (https://spacetime-environ.github.io/stepi2) that contains data, code and further worked examples. Features: • Explores the interface between environmental epidemiology and spatio­-temporal modeling • Incorporates examples that show how spatio-temporal methodology can inform societal concerns about the effects of environmental hazards on health • Uses a Bayesian foundation on which to build an integrated approach to spatio-temporal modeling and environmental epidemiology • Discusses data analysis and topics such as data visualization, mapping, wrangling and analysis • Shows how to design networks for monitoring hazardous environmental processes and the ill effects of preferential sampling • Through the listing and application of code, shows the power of R, tidyverse, NIMBLE and Stan and other modern tools in performing complex data analysis and modeling Representing a continuing important direction in environmental epidemiology, this book – in full color throughout – underscores the increasing need to consider dependencies in both space and time when modeling epidemiological data. Readers will learn how to identify and model patterns in spatio-temporal data and how to exploit dependencies over space and time to reduce bias and inefficiency when estimating risks to health.

The world is becoming increasingly complex, with larger quantities of data available to be analyzed. It so happens that much of these "big data" that are available are spatio-temporal in nature, meaning that they can be indexed by their spatial locations and time stamps. Spatio-Temporal Statistics with R provides an accessible introduction to statistical analysis of spatio-temporal data, with hands-on applications of the statistical methods using R Labs found at the end of each chapter. The book: Gives a step-by-step approach to analyzing spatio-temporal data, starting with visualization, then statistical modelling, with an emphasis on hierarchical statistical models and basis function expansions, and finishing with model evaluation Provides a gradual entry to the methodological aspects of spatio-temporal statistics Provides broad coverage of using R as well as "R Tips" throughout. Features detailed examples and applications in end-of-chapter Labs Features "Technical Notes" throughout to provide additional technical detail where relevant Supplemented by a website featuring the associated R package, data, reviews, errata, a discussion forum, and more The book fills a void in the literature and available software, providing a bridge for students and researchers alike who wish to learn the basics of spatio-temporal statistics. It is written in an informal style and functions as a down-to-earth introduction to the subject. Any reader familiar with calculus-based probability and statistics, and who is comfortable with basic matrix-algebra representations of statistical models, would find this book easy to follow. The goal is to give as many people as possible the tools and confidence to analyze spatio-temporal data.

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.

Winner of the 2013 DeGroot Prize. A state-of-the-art presentation of spatio-temporal processes, bridging classic ideas with modern hierarchical statistical modeling concepts and the latest computational methods Noel Cressie and Christopher K. Wikle, are also winners of the 2011 PROSE Award in the Mathematics category, for the book “Statistics for Spatio-Temporal Data” (2011), published by John Wiley and Sons. (The PROSE awards, for Professional and Scholarly Excellence, are given by the Association of American Publishers, the national trade association of the US book publishing industry.) Statistics for Spatio-Temporal Data has now been reprinted with small corrections to the text and the bibliography. The overall content and pagination of the new printing remains the same; the difference comes in the form of corrections to typographical errors, editing of incomplete and missing references, and some updated spatio-temporal interpretations. From understanding environmental processes and climate trends to developing new technologies for mapping public-health data and the spread of invasive-species, there is a high demand for statistical analyses of data that take spatial, temporal, and spatio-temporal information into account. Statistics for Spatio-Temporal Data presents a systematic approach to key quantitative techniques that incorporate the latest advances in statistical computing as well as hierarchical, particularly Bayesian, statistical modeling, with an emphasis on dynamical spatio-temporal models. Cressie and Wikle supply a unique presentation that incorporates ideas from the areas of time series and spatial statistics as well as stochastic processes. Beginning with separate treatments of temporal data and spatial data, the book combines these concepts to discuss spatio-temporal statistical methods for understanding complex processes. Topics of coverage include: Exploratory methods for spatio-temporal data, including visualization, spectral analysis, empirical orthogonal function analysis, and LISAs Spatio-temporal covariance functions, spatio-temporal kriging, and time series of spatial processes Development of hierarchical dynamical spatio-temporal models (DSTMs), with discussion of linear and nonlinear DSTMs and computational algorithms for their implementation Quantifying and exploring spatio-temporal variability in scientific applications, including case studies based on real-world environmental data Throughout the book, interesting applications demonstrate the relevance of the presented concepts. Vivid, full-color graphics emphasize the visual nature of the topic, and a related FTP site contains supplementary material. Statistics for Spatio-Temporal Data is an excellent book for a graduate-level course on spatio-temporal statistics. It is also a valuable reference for researchers and practitioners in the fields of applied mathematics, engineering, and the environmental and health sciences.

Handbook of Spatial Epidemiology explains how to model epidemiological problems and improve inference about disease etiology from a geographical perspective. Top epidemiologists, geographers, and statisticians share interdisciplinary viewpoints on analyzing spatial data and space-time variations in disease incidences. These analyses can provide imp

Progressively more and more attention has been paid to how location affects health outcomes. The area of disease mapping focusses on these problems, and the Bayesian paradigm has a major role to play in the understanding of the complex interplay of context and individual predisposition in such studies of disease. Using R for Bayesian Spatial and Spatio-Temporal Health Modeling provides a major resource for those interested in applying Bayesian methodology in small area health data studies. Features: Review of R graphics relevant to spatial health data Overview of Bayesian methods and Bayesian hierarchical modeling as applied to spatial data Bayesian Computation and goodness-of-fit Review of basic Bayesian disease mapping models Spatio-temporal modeling with MCMC and INLA Special topics include multivariate models, survival analysis, missing data, measurement error, variable selection, individual event modeling, and infectious disease modeling Software for fitting models based on BRugs, Nimble, CARBayes and INLA Provides code relevant to fitting all examples throughout the book at a supplementary website The book fills a void in the literature and available software, providing a crucial link for students and professionals alike to engage in the analysis of spatial and spatio-temporal health data from a Bayesian perspective using R. The book emphasizes the use of MCMC via Nimble, BRugs, and CARBAyes, but also includes INLA for comparative purposes. In addition, a wide range of packages useful in the analysis of geo-referenced spatial data are employed and code is provided. It will likely become a key reference for researchers and students from biostatistics, epidemiology, public health, and environmental science.

Applied sciences, both physical and social, such as atmospheric, biological, climate, demographic, economic, ecological, environmental, oceanic and political, routinely gather large volumes of spatial and spatio-temporal data in order to make wide ranging inference and prediction. Ideally such inferential tasks should be approached through modelling, which aids in estimation of uncertainties in all conclusions drawn from such data. Unified Bayesian modelling, implemented through user friendly software packages, provides a crucial key to unlocking the full power of these methods for solving challenging practical problems. Key features of the book: • Accessible detailed discussion of a majority of all aspects of Bayesian methods and computations with worked examples, numerical illustrations and exercises • A spatial statistics jargon buster chapter that enables the reader to build up a vocabulary without getting clouded in modeling and technicalities • Computation and modeling illustrations are provided with the help of the dedicated R package bmstdr, allowing the reader to use well-known packages and platforms, such as rstan, INLA, spBayes, spTimer, spTDyn, CARBayes, CARBayesST, etc • Included are R code notes detailing the algorithms used to produce all the tables and figures, with data and code available via an online supplement • Two dedicated chapters discuss practical examples of spatio-temporal modeling of point referenced and areal unit data • Throughout, the emphasis has been on validating models by splitting data into test and training sets following on the philosophy of machine learning and data science This book is designed to make spatio-temporal modeling and analysis accessible and understandable to a wide audience of students and researchers, from mathematicians and statisticians to practitioners in the applied sciences. It presents most of the modeling with the help of R commands written in a purposefully developed R package to facilitate spatio-temporal modeling. It does not compromise on rigour, as it presents the underlying theories of Bayesian inference and computation in standalone chapters, which would be appeal those interested in the theoretical details. By avoiding hard core mathematics and calculus, this book aims to be a bridge that removes the statistical knowledge gap from among the applied scientists.

This book clearly describes the many applications of graph theory to ecological questions, providing instruction and encouragement to researchers.