Advanced Spatial Modeling With Stochastic Partial Differential Equations Using R And Inla

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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 : 224 pages
File Size : 48,9 Mb
Release : 2018-12-07
Category : Mathematics
ISBN : 9780429628214

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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.

Bayesian inference with INLA

Virgilio Gomez-Rubio
Bayesian inference with INLA Book PDF

Author : Virgilio Gomez-Rubio
Publisher : CRC Press
Page : 316 pages
File Size : 55,8 Mb
Release : 2020-02-20
Category : Mathematics
ISBN : 9781351707206

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Bayesian inference with INLA by Virgilio Gomez-Rubio Pdf

The integrated nested Laplace approximation (INLA) is a recent computational method that can fit Bayesian models in a fraction of the time required by typical Markov chain Monte Carlo (MCMC) methods. INLA focuses on marginal inference on the model parameters of latent Gaussian Markov random fields models and exploits conditional independence properties in the model for computational speed. Bayesian Inference with INLA provides a description of INLA and its associated R package for model fitting. This book describes the underlying methodology as well as how to fit a wide range of models with R. Topics covered include generalized linear mixed-effects models, multilevel models, spatial and spatio-temporal models, smoothing methods, survival analysis, imputation of missing values, and mixture models. Advanced features of the INLA package and how to extend the number of priors and latent models available in the package are discussed. All examples in the book are fully reproducible and datasets and R code are available from the book website. This book will be helpful to researchers from different areas with some background in Bayesian inference that want to apply the INLA method in their work. The examples cover topics on biostatistics, econometrics, education, environmental science, epidemiology, public health, and the social sciences.

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 : 48,9 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

Geospatial Health Data

Paula Moraga
Geospatial Health Data Book PDF

Author : Paula Moraga
Publisher : CRC Press
Page : 217 pages
File Size : 53,9 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.

Bayesian Regression Modeling with INLA

Xiaofeng Wang,Yu Ryan Yue,Julian J. Faraway
Bayesian Regression Modeling with INLA Book PDF

Author : Xiaofeng Wang,Yu Ryan Yue,Julian J. Faraway
Publisher : CRC Press
Page : 325 pages
File Size : 52,8 Mb
Release : 2018-01-29
Category : Mathematics
ISBN : 9781351165747

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Bayesian Regression Modeling with INLA by Xiaofeng Wang,Yu Ryan Yue,Julian J. Faraway Pdf

INLA stands for Integrated Nested Laplace Approximations, which is a new method for fitting a broad class of Bayesian regression models. No samples of the posterior marginal distributions need to be drawn using INLA, so it is a computationally convenient alternative to Markov chain Monte Carlo (MCMC), the standard tool for Bayesian inference. Bayesian Regression Modeling with INLA covers a wide range of modern regression models and focuses on the INLA technique for building Bayesian models using real-world data and assessing their validity. A key theme throughout the book is that it makes sense to demonstrate the interplay of theory and practice with reproducible studies. Complete R commands are provided for each example, and a supporting website holds all of the data described in the book. An R package including the data and additional functions in the book is available to download. The book is aimed at readers who have a basic knowledge of statistical theory and Bayesian methodology. It gets readers up to date on the latest in Bayesian inference using INLA and prepares them for sophisticated, real-world work. Xiaofeng Wang is Professor of Medicine and Biostatistics at the Cleveland Clinic Lerner College of Medicine of Case Western Reserve University and a Full Staff in the Department of Quantitative Health Sciences at Cleveland Clinic. Yu Ryan Yue is Associate Professor of Statistics in the Paul H. Chook Department of Information Systems and Statistics at Baruch College, The City University of New York. Julian J. Faraway is Professor of Statistics in the Department of Mathematical Sciences at the University of Bath.

Gaussian Markov Random Fields

Havard Rue,Leonhard Held
Gaussian Markov Random Fields Book PDF

Author : Havard Rue,Leonhard Held
Publisher : CRC Press
Page : 280 pages
File Size : 46,6 Mb
Release : 2005-02-18
Category : Mathematics
ISBN : 9780203492024

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Gaussian Markov Random Fields by Havard Rue,Leonhard Held Pdf

Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studie

Dynamic Time Series Models using R-INLA

Nalini Ravishanker,Balaji Raman,Refik Soyer
Dynamic Time Series Models using R INLA Book PDF

Author : Nalini Ravishanker,Balaji Raman,Refik Soyer
Publisher : CRC Press
Page : 297 pages
File Size : 40,6 Mb
Release : 2022-08-10
Category : Mathematics
ISBN : 9781000622607

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Dynamic Time Series Models using R-INLA by Nalini Ravishanker,Balaji Raman,Refik Soyer Pdf

Dynamic Time Series Models using R-INLA: An Applied Perspective is the outcome of a joint effort to systematically describe the use of R-INLA for analysing time series and showcasing the code and description by several examples. This book introduces the underpinnings of R-INLA and the tools needed for modelling different types of time series using an approximate Bayesian framework. The book is an ideal reference for statisticians and scientists who work with time series data. It provides an excellent resource for teaching a course on Bayesian analysis using state space models for time series. Key Features: Introduction and overview of R-INLA for time series analysis. Gaussian and non-Gaussian state space models for time series. State space models for time series with exogenous predictors. Hierarchical models for a potentially large set of time series. Dynamic modelling of stochastic volatility and spatio-temporal dependence.

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 : 44,8 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.

Spatial Statistics for Data Science

Paula Moraga
Spatial Statistics for Data Science Book PDF

Author : Paula Moraga
Publisher : CRC Press
Page : 332 pages
File Size : 48,8 Mb
Release : 2023-12-08
Category : Mathematics
ISBN : 9781003832331

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Spatial Statistics for Data Science by Paula Moraga Pdf

Spatial data is crucial to improve decision-making in a wide range of fields including environment, health, ecology, urban planning, economy, and society. Spatial Statistics for Data Science: Theory and Practice with R describes statistical methods, modeling approaches, and visualization techniques to analyze spatial data using R. The book provides a comprehensive overview of the varying types of spatial data, and detailed explanations of the theoretical concepts of spatial statistics, alongside fully reproducible examples which demonstrate how to simulate, describe, and analyze spatial data in various applications. Combining theory and practice, the book includes real-world data science examples such as disease risk mapping, air pollution prediction, species distribution modeling, crime mapping, and real state analyses. The book utilizes publicly available data and offers clear explanations of the R code for importing, manipulating, analyzing, and visualizing data, as well as the interpretation of the results. This ensures contents are easily accessible and fully reproducible for students, researchers, and practitioners. Key Features: Describes R packages for retrieval, manipulation, and visualization of spatial data Offers a comprehensive overview of spatial statistical methods including spatial autocorrelation, clustering, spatial interpolation, model-based geostatistics, and spatial point processes Provides detailed explanations on how to fit and interpret Bayesian spatial models using the integrated nested Laplace approximation (INLA) and stochastic partial differential equation (SPDE) approaches

Recent Developments in Statistics and Data Science

Regina Bispo,Lígia Henriques-Rodrigues,Russell Alpizar-Jara,Miguel de Carvalho
Recent Developments in Statistics and Data Science Book PDF

Author : Regina Bispo,Lígia Henriques-Rodrigues,Russell Alpizar-Jara,Miguel de Carvalho
Publisher : Springer Nature
Page : 364 pages
File Size : 51,6 Mb
Release : 2022-11-28
Category : Mathematics
ISBN : 9783031127663

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Recent Developments in Statistics and Data Science by Regina Bispo,Lígia Henriques-Rodrigues,Russell Alpizar-Jara,Miguel de Carvalho Pdf

This volume presents a collection of twenty-five peer-reviewed articles carefully selected from the contributions presented at the XXV Congress of the Portuguese Statistical Society (2021). Containing state-of-the-art developments in theoretical and applied statistics, the book will be accessible to readers with a background in mathematics and statistics, but will also be of interest to researchers from other scientific disciplines (e.g., biology, economics, medicine), who will find a broad range of relevant applications.

Statistical Modeling Using Bayesian Latent Gaussian Models

Birgir Hrafnkelsson
Statistical Modeling Using Bayesian Latent Gaussian Models Book PDF

Author : Birgir Hrafnkelsson
Publisher : Springer Nature
Page : 256 pages
File Size : 53,9 Mb
Release : 2023-12-10
Category : Mathematics
ISBN : 9783031397912

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Statistical Modeling Using Bayesian Latent Gaussian Models by Birgir Hrafnkelsson Pdf

This book focuses on the statistical modeling of geophysical and environmental data using Bayesian latent Gaussian models. The structure of these models is described in a thorough introductory chapter, which explains how to construct prior densities for the model parameters, how to infer the parameters using Bayesian computation, and how to use the models to make predictions. The remaining six chapters focus on the application of Bayesian latent Gaussian models to real examples in glaciology, hydrology, engineering seismology, seismology, meteorology and climatology. These examples include: spatial predictions of surface mass balance; the estimation of Antarctica’s contribution to sea-level rise; the estimation of rating curves for the projection of water level to discharge; ground motion models for strong motion; spatial modeling of earthquake magnitudes; weather forecasting based on numerical model forecasts; and extreme value analysis of precipitation on a high-dimensional grid. The book is aimed at graduate students and experts in statistics, geophysics, environmental sciences, engineering, and related fields.

Theory of Spatial Statistics

M.N.M. van Lieshout
Theory of Spatial Statistics Book PDF

Author : M.N.M. van Lieshout
Publisher : CRC Press
Page : 162 pages
File Size : 55,9 Mb
Release : 2019-03-19
Category : Mathematics
ISBN : 9780429627033

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Theory of Spatial Statistics by M.N.M. van Lieshout Pdf

Theory of Spatial Statistics: A Concise Introduction presents the most important models used in spatial statistics, including random fields and point processes, from a rigorous mathematical point of view and shows how to carry out statistical inference. It contains full proofs, real-life examples and theoretical exercises. Solutions to the latter are available in an appendix. Assuming maturity in probability and statistics, these concise lecture notes are self-contained and cover enough material for a semester course. They may also serve as a reference book for researchers. Features * Presents the mathematical foundations of spatial statistics. * Contains worked examples from mining, disease mapping, forestry, soil and environmental science, and criminology. * Gives pointers to the literature to facilitate further study. * Provides example code in R to encourage the student to experiment. * Offers exercises and their solutions to test and deepen understanding. The book is suitable for postgraduate and advanced undergraduate students in mathematics and statistics.

Stochastic Differential Equations for Science and Engineering

Uffe Høgsbro Thygesen
Stochastic Differential Equations for Science and Engineering Book PDF

Author : Uffe Høgsbro Thygesen
Publisher : CRC Press
Page : 381 pages
File Size : 44,7 Mb
Release : 2023-06-15
Category : Mathematics
ISBN : 9781000884999

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Stochastic Differential Equations for Science and Engineering by Uffe Høgsbro Thygesen Pdf

Stochastic Differential Equations for Science and Engineering is aimed at students at the M.Sc. and PhD level. The book describes the mathematical construction of stochastic differential equations with a level of detail suitable to the audience, while also discussing applications to estimation, stability analysis, and control. The book includes numerous examples and challenging exercises. Computational aspects are central to the approach taken in the book, so the text is accompanied by a repository on GitHub containing a toolbox in R which implements algorithms described in the book, code that regenerates all figures, and solutions to exercises. Features: Contains numerous exercises, examples, and applications Suitable for science and engineering students at Master’s or PhD level Thorough treatment of the mathematical theory combined with an accessible treatment of motivating examples GitHub repository available at: https://github.com/Uffe-H-Thygesen/SDEbook and https://github.com/Uffe-H-Thygesen/SDEtools

The R Book

Michael J. Crawley
The R Book Book PDF

Author : Michael J. Crawley
Publisher : John Wiley & Sons
Page : 953 pages
File Size : 44,5 Mb
Release : 2007-06-13
Category : Mathematics
ISBN : 0470515066

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The R Book by Michael J. Crawley Pdf

The high-level language of R is recognized as one of the mostpowerful and flexible statistical software environments, and israpidly becoming the standard setting for quantitative analysis,statistics and graphics. R provides free access to unrivalledcoverage and cutting-edge applications, enabling the user to applynumerous statistical methods ranging from simple regression to timeseries or multivariate analysis. Building on the success of the author’s bestsellingStatistics: An Introduction using R, The R Book ispacked with worked examples, providing an all inclusive guide to R,ideal for novice and more accomplished users alike. The bookassumes no background in statistics or computing and introduces theadvantages of the R environment, detailing its applications in awide range of disciplines. Provides the first comprehensive reference manual for the Rlanguage, including practical guidance and full coverage of thegraphics facilities. Introduces all the statistical models covered by R, beginningwith simple classical tests such as chi-square and t-test. Proceeds to examine more advance methods, from regression andanalysis of variance, through to generalized linear models,generalized mixed models, time series, spatial statistics,multivariate statistics and much more. The R Book is aimed at undergraduates, postgraduates andprofessionals in science, engineering and medicine. It is alsoideal for students and professionals in statistics, economics,geography and the social sciences.

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 : 54,5 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.