Bayesian Inference With Inla

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Bayesian inference with INLA

Virgilio Gomez-Rubio
Bayesian inference with INLA Book PDF

Author : Virgilio Gomez-Rubio
Publisher : CRC Press
Page : 330 pages
File Size : 46,9 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.

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 : 312 pages
File Size : 40,5 Mb
Release : 2018-01-29
Category : Mathematics
ISBN : 9781351165754

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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.

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 : 48,6 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

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 : 40,9 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.

Geospatial Health Data

Paula Moraga
Geospatial Health Data Book PDF

Author : Paula Moraga
Publisher : CRC Press
Page : 217 pages
File Size : 46,8 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.

Complex Data Modeling and Computationally Intensive Statistical Methods

Pietro Mantovan,Piercesare Secchi
Complex Data Modeling and Computationally Intensive Statistical Methods Book PDF

Author : Pietro Mantovan,Piercesare Secchi
Publisher : Springer Science & Business Media
Page : 164 pages
File Size : 42,9 Mb
Release : 2011-01-27
Category : Computers
ISBN : 9788847013865

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Complex Data Modeling and Computationally Intensive Statistical Methods by Pietro Mantovan,Piercesare Secchi Pdf

Selected from the conference "S.Co.2009: Complex Data Modeling and Computationally Intensive Methods for Estimation and Prediction," these 20 papers cover the latest in statistical methods and computational techniques for complex and high dimensional datasets.

Computational Bayesian Statistics

M. Antónia Amaral Turkman,Carlos Daniel Paulino,Peter Müller
Computational Bayesian Statistics Book PDF

Author : M. Antónia Amaral Turkman,Carlos Daniel Paulino,Peter Müller
Publisher : Cambridge University Press
Page : 256 pages
File Size : 51,5 Mb
Release : 2019-02-28
Category : Business & Economics
ISBN : 9781108481038

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Computational Bayesian Statistics by M. Antónia Amaral Turkman,Carlos Daniel Paulino,Peter Müller Pdf

This integrated introduction to fundamentals, computation, and software is your key to understanding and using advanced Bayesian methods.

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 : 44,7 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.

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 : 46,9 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.

Statistical Modelling and Regression Structures

Thomas Kneib,Gerhard Tutz
Statistical Modelling and Regression Structures Book PDF

Author : Thomas Kneib,Gerhard Tutz
Publisher : Springer Science & Business Media
Page : 472 pages
File Size : 48,5 Mb
Release : 2010-01-12
Category : Mathematics
ISBN : 9783790824131

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Statistical Modelling and Regression Structures by Thomas Kneib,Gerhard Tutz Pdf

The contributions collected in this book have been written by well-known statisticians to acknowledge Ludwig Fahrmeir's far-reaching impact on Statistics as a science, while celebrating his 65th birthday. The contributions cover broad areas of contemporary statistical model building, including semiparametric and geoadditive regression, Bayesian inference in complex regression models, time series modelling, statistical regularization, graphical models and stochastic volatility models.

Bayesian Modeling and Computation in Python

Osvaldo A. Martin,Ravin Kumar,Junpeng Lao
Bayesian Modeling and Computation in Python Book PDF

Author : Osvaldo A. Martin,Ravin Kumar,Junpeng Lao
Publisher : CRC Press
Page : 420 pages
File Size : 48,8 Mb
Release : 2021-12-28
Category : Computers
ISBN : 9781000520040

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Bayesian Modeling and Computation in Python by Osvaldo A. Martin,Ravin Kumar,Junpeng Lao Pdf

Bayesian Modeling and Computation in Python aims to help beginner Bayesian practitioners to become intermediate modelers. It uses a hands on approach with PyMC3, Tensorflow Probability, ArviZ and other libraries focusing on the practice of applied statistics with references to the underlying mathematical theory. The book starts with a refresher of the Bayesian Inference concepts. The second chapter introduces modern methods for Exploratory Analysis of Bayesian Models. With an understanding of these two fundamentals the subsequent chapters talk through various models including linear regressions, splines, time series, Bayesian additive regression trees. The final chapters include Approximate Bayesian Computation, end to end case studies showing how to apply Bayesian modelling in different settings, and a chapter about the internals of probabilistic programming languages. Finally the last chapter serves as a reference for the rest of the book by getting closer into mathematical aspects or by extending the discussion of certain topics. This book is written by contributors of PyMC3, ArviZ, Bambi, and Tensorflow Probability among other libraries.

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 : 42,7 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

Bayes Rules!

Alicia A. Johnson,Miles Q. Ott,Mine Dogucu
Bayes Rules Book PDF

Author : Alicia A. Johnson,Miles Q. Ott,Mine Dogucu
Publisher : CRC Press
Page : 606 pages
File Size : 50,5 Mb
Release : 2022-03-03
Category : Mathematics
ISBN : 9781000529562

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Bayes Rules! by Alicia A. Johnson,Miles Q. Ott,Mine Dogucu Pdf

Praise for Bayes Rules!: An Introduction to Applied Bayesian Modeling “A thoughtful and entertaining book, and a great way to get started with Bayesian analysis.” Andrew Gelman, Columbia University “The examples are modern, and even many frequentist intro books ignore important topics (like the great p-value debate) that the authors address. The focus on simulation for understanding is excellent.” Amy Herring, Duke University “I sincerely believe that a generation of students will cite this book as inspiration for their use of – and love for – Bayesian statistics. The narrative holds the reader’s attention and flows naturally – almost conversationally. Put simply, this is perhaps the most engaging introductory statistics textbook I have ever read. [It] is a natural choice for an introductory undergraduate course in applied Bayesian statistics." Yue Jiang, Duke University “This is by far the best book I’ve seen on how to (and how to teach students to) do Bayesian modeling and understand the underlying mathematics and computation. The authors build intuition and scaffold ideas expertly, using interesting real case studies, insightful graphics, and clear explanations. The scope of this book is vast – from basic building blocks to hierarchical modeling, but the authors’ thoughtful organization allows the reader to navigate this journey smoothly. And impressively, by the end of the book, one can run sophisticated Bayesian models and actually understand the whys, whats, and hows.” Paul Roback, St. Olaf College “The authors provide a compelling, integrated, accessible, and non-religious introduction to statistical modeling using a Bayesian approach. They outline a principled approach that features computational implementations and model assessment with ethical implications interwoven throughout. Students and instructors will find the conceptual and computational exercises to be fresh and engaging.” Nicholas Horton, Amherst College An engaging, sophisticated, and fun introduction to the field of Bayesian statistics, Bayes Rules!: An Introduction to Applied Bayesian Modeling brings the power of modern Bayesian thinking, modeling, and computing to a broad audience. In particular, the book is an ideal resource for advanced undergraduate statistics students and practitioners with comparable experience. Bayes Rules! empowers readers to weave Bayesian approaches into their everyday practice. Discussions and applications are data driven. A natural progression from fundamental to multivariable, hierarchical models emphasizes a practical and generalizable model building process. The evaluation of these Bayesian models reflects the fact that a data analysis does not exist in a vacuum. Features • Utilizes data-driven examples and exercises. • Emphasizes the iterative model building and evaluation process. • Surveys an interconnected range of multivariable regression and classification models. • Presents fundamental Markov chain Monte Carlo simulation. • Integrates R code, including RStan modeling tools and the bayesrules package. • Encourages readers to tap into their intuition and learn by doing. • Provides a friendly and inclusive introduction to technical Bayesian concepts. • Supports Bayesian applications with foundational Bayesian theory.

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 : 358 pages
File Size : 55,7 Mb
Release : 2022-08-10
Category : Mathematics
ISBN : 9781000622874

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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 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 : 52,9 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.