Using R For Bayesian Spatial And Spatio Temporal Health Modeling

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Using R for Bayesian Spatial and Spatio-Temporal Health Modeling

Andrew B. Lawson
Using R for Bayesian Spatial and Spatio Temporal Health Modeling Book PDF

Author : Andrew B. Lawson
Publisher : CRC Press
Page : 300 pages
File Size : 50,7 Mb
Release : 2021-04-28
Category : Mathematics
ISBN : 9781000376708

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Using R for Bayesian Spatial and Spatio-Temporal Health Modeling by Andrew B. Lawson Pdf

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.

Spatial and Spatio-temporal Bayesian Models with R - INLA

Marta Blangiardo,Michela Cameletti
Spatial and Spatio temporal Bayesian Models with R INLA Book PDF

Author : Marta Blangiardo,Michela Cameletti
Publisher : John Wiley & Sons
Page : 321 pages
File Size : 42,5 Mb
Release : 2015-06-02
Category : Mathematics
ISBN : 9781118326558

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Spatial and Spatio-temporal Bayesian Models with R - INLA by Marta Blangiardo,Michela Cameletti Pdf

Spatial and Spatio-Temporal Bayesian Models with R-INLA provides a much needed, practically oriented & innovative presentation of the combination of Bayesian methodology and spatial statistics. The authors combine an introduction to Bayesian theory and methodology with a focus on the spatial and spatio­-temporal models used within the Bayesian framework and a series of practical examples which allow the reader to link the statistical theory presented to real data problems. The numerous examples from the fields of epidemiology, biostatistics and social science all are coded in the R package R-INLA, which has proven to be a valid alternative to the commonly used Markov Chain Monte Carlo simulations

Bayesian Modeling of Spatio-Temporal Data with R

Sujit Sahu
Bayesian Modeling of Spatio Temporal Data with R Book PDF

Author : Sujit Sahu
Publisher : CRC Press
Page : 385 pages
File Size : 51,7 Mb
Release : 2022-02-23
Category : Mathematics
ISBN : 9781000543698

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Bayesian Modeling of Spatio-Temporal Data with R by Sujit Sahu Pdf

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.

Geospatial Health Data

Paula Moraga
Geospatial Health Data Book PDF

Author : Paula Moraga
Publisher : CRC Press
Page : 217 pages
File Size : 45,7 Mb
Release : 2019-11-26
Category : Medical
ISBN : 9781000732153

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Geospatial Health Data by Paula Moraga Pdf

Geospatial health data are essential to inform public health and policy. These data can be used to quantify disease burden, understand geographic and temporal patterns, identify risk factors, and measure inequalities. Geospatial Health Data: Modeling and Visualization with R-INLA and Shiny describes spatial and spatio-temporal statistical methods and visualization techniques to analyze georeferenced health data in R. The book covers the following topics: Manipulate and transform point, areal, and raster data, Bayesian hierarchical models for disease mapping using areal and geostatistical data, Fit and interpret spatial and spatio-temporal models with the Integrated Nested Laplace Approximations (INLA) and the Stochastic Partial Differential Equation (SPDE) approaches, Create interactive and static visualizations such as disease maps and time plots, Reproducible R Markdown reports, interactive dashboards, and Shiny web applications that facilitate the communication of insights to collaborators and policy makers. The book features fully reproducible examples of several disease and environmental applications using real-world data such as malaria in The Gambia, cancer in Scotland and USA, and air pollution in Spain. Examples in the book focus on health applications, but the approaches covered are also applicable to other fields that use georeferenced data including epidemiology, ecology, demography or criminology. The book provides clear descriptions of the R code for data importing, manipulation, modeling and visualization, as well as the interpretation of the results. This ensures contents are fully reproducible and accessible for students, researchers and practitioners.

Regression Modelling wih Spatial and Spatial-Temporal Data

Robert P. Haining,Guangquan Li
Regression Modelling wih Spatial and Spatial Temporal Data Book PDF

Author : Robert P. Haining,Guangquan Li
Publisher : CRC Press
Page : 527 pages
File Size : 55,7 Mb
Release : 2020-01-27
Category : Mathematics
ISBN : 9780429529108

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Regression Modelling wih Spatial and Spatial-Temporal Data by Robert P. Haining,Guangquan Li Pdf

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 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.

Spatio-Temporal Methods in Environmental Epidemiology

Gavin Shaddick,James V. Zidek
Spatio Temporal Methods in Environmental Epidemiology Book PDF

Author : Gavin Shaddick,James V. Zidek
Publisher : CRC Press
Page : 395 pages
File Size : 42,5 Mb
Release : 2015-06-17
Category : Mathematics
ISBN : 9781482237047

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Spatio-Temporal Methods in Environmental Epidemiology by Gavin Shaddick,James V. Zidek Pdf

Teaches Students How to Perform Spatio-Temporal Analyses within Epidemiological Studies Spatio-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 environmental epidemiologists, the book links recent developments in spatio-temporal methodology with epidemiological applications. Drawing on real-life problems, it provides the necessary tools to exploit advances in methodology when assessing the health risks associated with environmental hazards. The book’s clear guidelines enable the implementation of the methodology and estimation of risks in practice. Designed for graduate students in both epidemiology and statistics, the text covers a wide range of topics, from an introduction to epidemiological principles and the foundations of spatio-temporal modeling to new research directions. It describes traditional and Bayesian approaches and presents the theory of spatial, temporal, and spatio-temporal modeling in the context of its application to environmental epidemiology. The text includes practical examples together with embedded R code, details of specific R packages, and the use of other software, such as WinBUGS/OpenBUGS and integrated nested Laplace approximations (INLA). A supplementary website provides additional code, data, examples, exercises, lab projects, and more. Representing a major new 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. Students will learn how to identify and model patterns in spatio-temporal data as well as exploit dependencies over space and time to reduce bias and inefficiency.

Spatial and Spatio-temporal Bayesian Models with R - INLA

Marta Blangiardo,Michela Cameletti
Spatial and Spatio temporal Bayesian Models with R INLA Book PDF

Author : Marta Blangiardo,Michela Cameletti
Publisher : John Wiley & Sons
Page : 320 pages
File Size : 48,8 Mb
Release : 2015-04-07
Category : Mathematics
ISBN : 9781118950197

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Spatial and Spatio-temporal Bayesian Models with R - INLA by Marta Blangiardo,Michela Cameletti Pdf

Spatial and Spatio-Temporal Bayesian Models withR-INLA provides a much needed, practically oriented& innovative presentation of the combination of Bayesianmethodology and spatial statistics. The authors combine anintroduction to Bayesian theory and methodology with a focus on thespatial and spatio­-temporal models used within the Bayesianframework and a series of practical examples which allow the readerto link the statistical theory presented to real data problems. Thenumerous examples from the fields of epidemiology, biostatisticsand social science all are coded in the R package R-INLA, which hasproven to be a valid alternative to the commonly used Markov ChainMonte Carlo simulations

Spatio–Temporal Methods in Environmental Epidemiology with R

Gavin Shaddick,James V. Zidek,Alexandra M. Schmidt
Spatio Temporal Methods in Environmental Epidemiology with R Book PDF

Author : Gavin Shaddick,James V. Zidek,Alexandra M. Schmidt
Publisher : CRC Press
Page : 458 pages
File Size : 50,7 Mb
Release : 2023-12-12
Category : Medical
ISBN : 9781003808022

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Spatio–Temporal Methods in Environmental Epidemiology with R by Gavin Shaddick,James V. Zidek,Alexandra M. Schmidt Pdf

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.

Spatio-Temporal Statistics with R

Christopher K. Wikle,Andrew Zammit-Mangion,Noel Cressie
Spatio Temporal Statistics with R Book PDF

Author : Christopher K. Wikle,Andrew Zammit-Mangion,Noel Cressie
Publisher : CRC Press
Page : 380 pages
File Size : 50,7 Mb
Release : 2019-02-18
Category : Mathematics
ISBN : 9780429649783

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Spatio-Temporal Statistics with R by Christopher K. Wikle,Andrew Zammit-Mangion,Noel Cressie Pdf

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.

Bayesian Disease Mapping

Andrew B. Lawson
Bayesian Disease Mapping Book PDF

Author : Andrew B. Lawson
Publisher : CRC Press
Page : 398 pages
File Size : 53,6 Mb
Release : 2013-03-18
Category : Mathematics
ISBN : 9781466504813

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Bayesian Disease Mapping by Andrew B. Lawson Pdf

Since the publication of the first edition, many new Bayesian tools and methods have been developed for space-time data analysis, the predictive modeling of health outcomes, and other spatial biostatistical areas. Exploring these new developments, Bayesian Disease Mapping: Hierarchical Modeling in Spatial Epidemiology, Second Edition provides an up-to-date, cohesive account of the full range of Bayesian disease mapping methods and applications. A biostatistics professor and WHO advisor, the author illustrates the use of Bayesian hierarchical modeling in the geographical analysis of disease through a range of real-world datasets. New to the Second Edition Three new chapters on regression and ecological analysis, putative hazard modeling, and disease map surveillance Expanded material on case event modeling and spatiotemporal analysis New and updated examples Two new appendices featuring examples of integrated nested Laplace approximation (INLA) and conditional autoregressive (CAR) models In addition to these new topics, the book covers more conventional areas such as relative risk estimation, clustering, spatial survival analysis, and longitudinal analysis. After an introduction to Bayesian inference, computation, and model assessment, the text focuses on important themes, including disease map reconstruction, cluster detection, regression and ecological analysis, putative hazard modeling, analysis of multiple scales and multiple diseases, spatial survival and longitudinal studies, spatiotemporal methods, and map surveillance. It shows how Bayesian disease mapping can yield significant insights into georeferenced health data. WinBUGS and R are used throughout for data manipulation and simulation.

Handbook of Spatial Epidemiology

Andrew B. Lawson,Sudipto Banerjee,Robert P. Haining,Maria Dolores Ugarte
Handbook of Spatial Epidemiology Book PDF

Author : Andrew B. Lawson,Sudipto Banerjee,Robert P. Haining,Maria Dolores Ugarte
Publisher : CRC Press
Page : 704 pages
File Size : 55,7 Mb
Release : 2016-04-06
Category : Mathematics
ISBN : 9781482253023

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Handbook of Spatial Epidemiology by Andrew B. Lawson,Sudipto Banerjee,Robert P. Haining,Maria Dolores Ugarte Pdf

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

Disease Mapping

Miguel A. Martinez-Beneito,Paloma Botella-Rocamora
Disease Mapping Book PDF

Author : Miguel A. Martinez-Beneito,Paloma Botella-Rocamora
Publisher : CRC Press
Page : 371 pages
File Size : 48,7 Mb
Release : 2019-07-02
Category : Mathematics
ISBN : 9781351645027

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Disease Mapping by Miguel A. Martinez-Beneito,Paloma Botella-Rocamora Pdf

Disease Mapping: From Foundations to Multidimensional Modeling guides the reader from the basics of disease mapping to the most advanced topics in this field. A multidimensional framework is offered that makes possible the joint modeling of several risks patterns corresponding to combinations of several factors, including age group, time period, disease, etc. Although theory will be covered, the applied component will be equally as important with lots of practical examples offered. Features: Discusses the very latest developments on multivariate and multidimensional mapping. Gives a single state-of-the-art framework that unifies most of the previously proposed disease mapping approaches. Balances epidemiological and statistical points-of-view. Requires no previous knowledge of disease mapping. Includes practical sessions at the end of each chapter with WinBUGs/INLA and real world datasets. Supplies R code for the examples in the book so that they can be reproduced by the reader. About the Authors: Miguel A. Martinez Beneito has spent his whole career working as a statistician for public health services, first at the epidemiology unit of the Valencia (Spain) regional health administration and later as a researcher at the public health division of FISABIO, a regional bio-sanitary research center. He has been also the Bayesian Hierarchical Models professor for several seasons at the University of Valencia Biostatics Master. Paloma Botella Rocamora has spent most of her professional career in academia although she now works as a statistician for the epidemiology unit of the Valencia regional health administration. Most of her research has been devoted to developing and applying disease mapping models to real data, although her work as a statistician in an epidemiology unit makes her develop and apply statistical methods to health data, in general.

Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA

Elias T. Krainski,Virgilio Gómez-Rubio,Haakon Bakka,Amanda Lenzi,Daniela Castro-Camilo,Daniel Simpson,Finn Lindgren,Håvard Rue
Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA Book PDF

Author : Elias T. Krainski,Virgilio Gómez-Rubio,Haakon Bakka,Amanda Lenzi,Daniela Castro-Camilo,Daniel Simpson,Finn Lindgren,Håvard Rue
Publisher : CRC Press
Page : 284 pages
File Size : 53,8 Mb
Release : 2018-12-07
Category : Mathematics
ISBN : 9780429629853

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Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA by Elias T. Krainski,Virgilio Gómez-Rubio,Haakon Bakka,Amanda Lenzi,Daniela Castro-Camilo,Daniel Simpson,Finn Lindgren,Håvard Rue Pdf

Modeling spatial and spatio-temporal continuous processes is an important and challenging problem in spatial statistics. Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA describes in detail the stochastic partial differential equations (SPDE) approach for modeling continuous spatial processes with a Matérn covariance, which has been implemented using the integrated nested Laplace approximation (INLA) in the R-INLA package. Key concepts about modeling spatial processes and the SPDE approach are explained with examples using simulated data and real applications. This book has been authored by leading experts in spatial statistics, including the main developers of the INLA and SPDE methodologies and the R-INLA package. It also includes a wide range of applications: * Spatial and spatio-temporal models for continuous outcomes * Analysis of spatial and spatio-temporal point patterns * Coregionalization spatial and spatio-temporal models * Measurement error spatial models * Modeling preferential sampling * Spatial and spatio-temporal models with physical barriers * Survival analysis with spatial effects * Dynamic space-time regression * Spatial and spatio-temporal models for extremes * Hurdle models with spatial effects * Penalized Complexity priors for spatial models All the examples in the book are fully reproducible. Further information about this book, as well as the R code and datasets used, is available from the book website at http://www.r-inla.org/spde-book. The tools described in this book will be useful to researchers in many fields such as biostatistics, spatial statistics, environmental sciences, epidemiology, ecology and others. Graduate and Ph.D. students will also find this book and associated files a valuable resource to learn INLA and the SPDE approach for spatial modeling.

Spatiotemporal Analysis of Air Pollution and Its Application in Public Health

Lixin Li,Xiaolu Zhou,Weitian Tong
Spatiotemporal Analysis of Air Pollution and Its Application in Public Health Book PDF

Author : Lixin Li,Xiaolu Zhou,Weitian Tong
Publisher : Elsevier
Page : 336 pages
File Size : 55,6 Mb
Release : 2019-11-13
Category : Computers
ISBN : 9780128165263

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Spatiotemporal Analysis of Air Pollution and Its Application in Public Health by Lixin Li,Xiaolu Zhou,Weitian Tong Pdf

Spatiotemporal Analysis of Air Pollution and Its Application in Public Health reviews, in detail, the tools needed to understand the spatial temporal distribution and trends of air pollution in the atmosphere, including how this information can be tied into the diverse amount of public health data available using accurate GIS techniques. By utilizing GIS to monitor, analyze and visualize air pollution problems, it has proven to not only be the most powerful, accurate and flexible way to understand the atmosphere, but also a great way to understand the impact air pollution has in diverse populations. This book is essential reading for novices and experts in atmospheric science, geography and any allied fields investigating air pollution. Introduces readers to the benefits and uses of geo-spatiotemporal analyses of big data to reveal new and greater understanding of the intersection of air pollution and health Ties in machine learning to improve speed and efficacy of data models Includes developing visualizations, historical data, and real-time air pollution in large geographic areas

Modelling Spatial and Spatial-Temporal Data: A Bayesian Approach

Robert P. Haining,Guangquan Li
Modelling Spatial and Spatial Temporal Data A Bayesian Approach Book PDF

Author : Robert P. Haining,Guangquan Li
Publisher : CRC Press
Page : 641 pages
File Size : 45,8 Mb
Release : 2020-01-27
Category : Mathematics
ISBN : 9781482237436

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Modelling Spatial and Spatial-Temporal Data: A Bayesian Approach by Robert P. Haining,Guangquan Li Pdf

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 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.