Download or read book Bayesian Spatial Modelling with Conjugate Prior Models written by Henning Omre and published by Springer Nature. This book was released on with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Bayesian inference with INLA written by Virgilio Gomez-Rubio and published by CRC Press. This book was released on 2020-02-20 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Bayesian Data Analysis Third Edition written by Andrew Gelman and published by CRC Press. This book was released on 2013-11-01 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice. New to the Third Edition Four new chapters on nonparametric modeling Coverage of weakly informative priors and boundary-avoiding priors Updated discussion of cross-validation and predictive information criteria Improved convergence monitoring and effective sample size calculations for iterative simulation Presentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagation New and revised software code The book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.

Download or read book Bayesian Model Selection and Statistical Modeling written by Tomohiro Ando and published by CRC Press. This book was released on 2010-05-27 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Along with many practical applications, Bayesian Model Selection and Statistical Modeling presents an array of Bayesian inference and model selection procedures. It thoroughly explains the concepts, illustrates the derivations of various Bayesian model selection criteria through examples, and provides R code for implementation. The author shows how to implement a variety of Bayesian inference using R and sampling methods, such as Markov chain Monte Carlo. He covers the different types of simulation-based Bayesian model selection criteria, including the numerical calculation of Bayes factors, the Bayesian predictive information criterion, and the deviance information criterion. He also provides a theoretical basis for the analysis of these criteria. In addition, the author discusses how Bayesian model averaging can simultaneously treat both model and parameter uncertainties. Selecting and constructing the appropriate statistical model significantly affect the quality of results in decision making, forecasting, stochastic structure explorations, and other problems. Helping you choose the right Bayesian model, this book focuses on the framework for Bayesian model selection and includes practical examples of model selection criteria.

Download or read book Scalable Bayesian spatial analysis with Gaussian Markov random fields written by Per Sidén and published by Linköping University Electronic Press. This book was released on 2020-08-17 with total page 53 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accurate statistical analysis of spatial data is important in many applications. Failing to properly account for spatial autocorrelation may often lead to false conclusions. At the same time, the ever-increasing sizes of spatial datasets pose a great computational challenge, as many standard methods for spatial analysis are limited to a few thousand data points. In this thesis, we explore how Gaussian Markov random fields (GMRFs) can be used for scalable analysis of spatial data. GMRFs are closely connected to the commonly used Gaussian processes, but have sparsity properties that make them computationally cheap both in time and memory. The Bayesian framework enables a GMRF to be used as a spatial prior, comprising the assumption of smooth variation over space, and gives a principled way to estimate the parameters and propagate uncertainty. We develop new algorithms that enable applying GMRF priors in 3D to the brain activity inherent in functional magnetic resonance imaging (fMRI) data, with millions of observations. We show that our methods are both faster and more accurate than previous work. A method for approximating selected elements of the inverse precision matrix (i.e. the covariance matrix) is also proposed, which is important for evaluating the posterior uncertainty. In addition, we establish a link between GMRFs and deep convolutional neural networks, which have been successfully used in countless machine learning tasks for images, resulting in a deep GMRF model. Finally, we show how GMRFs can be used in real-time robotic search and rescue operations, for modeling the spatial distribution of injured persons. Tillförlitlig statistisk analys av spatiala data är viktigt inom många tillämpningar. Om inte korrekt hänsyn tas till spatial autokorrelation kan det ofta leda till felaktiga slutsatser. Samtidigt ökar ständigt storleken på de spatiala datamaterialen vilket utgör en stor beräkningsmässig utmaning, eftersom många standardmetoder för spatial analys är begränsade till några tusental datapunkter. I denna avhandling utforskar vi hur Gaussiska Markov-fält (eng: Gaussian Markov random fields, GMRF) kan användas för mer skalbara analyser av spatiala data. GMRF-modeller är nära besläktade med de ofta använda Gaussiska processerna, men har gleshetsegenskaper som gör dem beräkningsmässigt effektiva både vad gäller tids- och minnesåtgång. Det Bayesianska synsättet gör det möjligt att använda GMRF som en spatial prior som innefattar antagandet om långsam spatial variation och ger ett principiellt tillvägagångssätt för att skatta parametrar och propagera osäkerhet. Vi utvecklar nya algoritmer som gör det möjligt att använda GMRF-priors i 3D för den hjärnaktivitet som indirekt kan observeras i hjärnbilder framtagna med tekniken fMRI, som innehåller milliontals datapunkter. Vi visar att våra metoder är både snabbare och mer korrekta än tidigare forskning. En metod för att approximera utvalda element i den inversa precisionsmatrisen (dvs. kovariansmatrisen) framförs också, vilket är viktigt för att kunna evaluera osäkerheten i posteriorn. Vidare gör vi en koppling mellan GMRF och djupa neurala faltningsnätverk, som har använts framgångsrikt för mängder av bildrelaterade problem inom maskininlärning, vilket mynnar ut i en djup GMRF-modell. Slutligen visar vi hur GMRF kan användas i realtid av autonoma drönare för räddningsinsatser i katastrofområden för att modellera den spatiala fördelningen av skadade personer.

Download or read book Spatial and Spatio temporal Bayesian Models with R INLA written by Marta Blangiardo and published by John Wiley & Sons. This book was released on 2015-06-02 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Statistical Methods for Spatial Data Analysis written by Oliver Schabenberger and published by CRC Press. This book was released on 2017-01-27 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding spatial statistics requires tools from applied and mathematical statistics, linear model theory, regression, time series, and stochastic processes. It also requires a mindset that focuses on the unique characteristics of spatial data and the development of specialized analytical tools designed explicitly for spatial data analysis. Statistical Methods for Spatial Data Analysis answers the demand for a text that incorporates all of these factors by presenting a balanced exposition that explores both the theoretical foundations of the field of spatial statistics as well as practical methods for the analysis of spatial data. This book is a comprehensive and illustrative treatment of basic statistical theory and methods for spatial data analysis, employing a model-based and frequentist approach that emphasizes the spatial domain. It introduces essential tools and approaches including: measures of autocorrelation and their role in data analysis; the background and theoretical framework supporting random fields; the analysis of mapped spatial point patterns; estimation and modeling of the covariance function and semivariogram; a comprehensive treatment of spatial analysis in the spectral domain; and spatial prediction and kriging. The volume also delivers a thorough analysis of spatial regression, providing a detailed development of linear models with uncorrelated errors, linear models with spatially-correlated errors and generalized linear mixed models for spatial data. It succinctly discusses Bayesian hierarchical models and concludes with reviews on simulating random fields, non-stationary covariance, and spatio-temporal processes. Additional material on the CRC Press website supplements the content of this book. The site provides data sets used as examples in the text, software code that can be used to implement many of the principal methods described and illustrated, and updates to the text itself.

Download or read book Applied Bayesian Modelling written by Peter Congdon and published by John Wiley & Sons. This book was released on 2014-05-23 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible approach to Bayesian computing and data analysis, with an emphasis on the interpretation of real data sets. Following in the tradition of the successful first edition, this book aims to make a wide range of statistical modeling applications accessible using tested code that can be readily adapted to the reader's own applications. The second edition has been thoroughly reworked and updated to take account of advances in the field. A new set of worked examples is included. The novel aspect of the first edition was the coverage of statistical modeling using WinBUGS and OPENBUGS. This feature continues in the new edition along with examples using R to broaden appeal and for completeness of coverage.

Download or read book Bayesian Machine Learning in Geotechnical Site Characterization written by Jianye Ching and published by CRC Press. This book was released on 2024-08-07 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian data analysis and modelling linked with machine learning offers a new tool for handling geotechnical data. This book presents recent advancements made by the author in the area of probabilistic geotechnical site characterization. Two types of correlation play central roles in geotechnical site characterization: cross-correlation among soil properties and spatial-correlation in the underground space. The book starts with the introduction of Bayesian notion of probability “degree of belief”, showing that well-known probability axioms can be obtained by Boolean logic and the definition of plausibility function without the use of the notion “relative frequency”. It then reviews probability theories and useful probability models for cross-correlation and spatial correlation. Methods for Bayesian parameter estimation and prediction are also presented, and the use of these methods demonstrated with geotechnical site characterization examples. Bayesian Machine Learning in Geotechnical Site Characterization suits consulting engineers and graduate students in the area.

Download or read book Bayesian Statistical Methods written by Brian J. Reich and published by CRC Press. This book was released on 2019-04-12 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian Statistical Methods provides data scientists with the foundational and computational tools needed to carry out a Bayesian analysis. This book focuses on Bayesian methods applied routinely in practice including multiple linear regression, mixed effects models and generalized linear models (GLM). The authors include many examples with complete R code and comparisons with analogous frequentist procedures. In addition to the basic concepts of Bayesian inferential methods, the book covers many general topics: Advice on selecting prior distributions Computational methods including Markov chain Monte Carlo (MCMC) Model-comparison and goodness-of-fit measures, including sensitivity to priors Frequentist properties of Bayesian methods Case studies covering advanced topics illustrate the flexibility of the Bayesian approach: Semiparametric regression Handling of missing data using predictive distributions Priors for high-dimensional regression models Computational techniques for large datasets Spatial data analysis The advanced topics are presented with sufficient conceptual depth that the reader will be able to carry out such analysis and argue the relative merits of Bayesian and classical methods. A repository of R code, motivating data sets, and complete data analyses are available on the book’s website. Brian J. Reich, Associate Professor of Statistics at North Carolina State University, is currently the editor-in-chief of the Journal of Agricultural, Biological, and Environmental Statistics and was awarded the LeRoy & Elva Martin Teaching Award. Sujit K. Ghosh, Professor of Statistics at North Carolina State University, has over 22 years of research and teaching experience in conducting Bayesian analyses, received the Cavell Brownie mentoring award, and served as the Deputy Director at the Statistical and Applied Mathematical Sciences Institute.

Download or read book Bayesian Nonparametrics written by J.K. Ghosh and published by Springer Science & Business Media. This book was released on 2006-05-11 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first systematic treatment of Bayesian nonparametric methods and the theory behind them. It will also appeal to statisticians in general. The book is primarily aimed at graduate students and can be used as the text for a graduate course in Bayesian non-parametrics.

Download or read book Handbook of Applied Spatial Analysis written by Manfred M. Fischer and published by Springer Science & Business Media. This book was released on 2009-12-24 with total page 801 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook is written for academics, researchers, practitioners and advanced graduate students. It has been designed to be read by those new or starting out in the field of spatial analysis as well as by those who are already familiar with the field. The chapters have been written in such a way that readers who are new to the field will gain important overview and insight. At the same time, those readers who are already practitioners in the field will gain through the advanced and/or updated tools and new materials and state-of-the-art developments included. This volume provides an accounting of the diversity of current and emergent approaches, not available elsewhere despite the many excellent journals and te- books that exist. Most of the chapters are original, some few are reprints from the Journal of Geographical Systems, Geographical Analysis, The Review of Regional Studies and Letters of Spatial and Resource Sciences. We let our contributors - velop, from their particular perspective and insights, their own strategies for m- ping the part of terrain for which they were responsible. As the chapters were submitted, we became the first consumers of the project we had initiated. We gained from depth, breadth and distinctiveness of our contributors’ insights and, in particular, the presence of links between them.

Download or read book Modelling Spatial and Spatial Temporal Data A Bayesian Approach written by Robert P. Haining and published by CRC Press. This book was released on 2020-01-27 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Kendall s Advanced Theory of Statistic 2B written by Anthony O'Hagan and published by John Wiley & Sons. This book was released on 2010-03-08 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kendall's Advanced Theory of Statistics and Kendall's Library of Statistics The development of modern statistical theory in the past fifty years is reflected in the history of the late Sir Maurice Kenfall's volumes The Advanced Theory of Statistics. The Advanced Theory began life as a two-volume work, and since its first appearance in 1943, has been an indispensable source for the core theory of classical statistics. With Bayesian Inference, the same high standard has been applied to this important and exciting new body of theory.

Download or read book Bayesian Modeling of Spatio Temporal Data with R written by Sujit Sahu and published by CRC Press. This book was released on 2022-02-23 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Applied Spatial Statistics for Public Health Data written by Lance A. Waller and published by John Wiley & Sons. This book was released on 2004-07-29 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: While mapped data provide a common ground for discussions between the public, the media, regulatory agencies, and public health researchers, the analysis of spatially referenced data has experienced a phenomenal growth over the last two decades, thanks in part to the development of geographical information systems (GISs). This is the first thorough overview to integrate spatial statistics with data management and the display capabilities of GIS. It describes methods for assessing the likelihood of observed patterns and quantifying the link between exposures and outcomes in spatially correlated data. This introductory text is designed to serve as both an introduction for the novice and a reference for practitioners in the field Requires only minimal background in public health and only some knowledge of statistics through multiple regression Touches upon some advanced topics, such as random effects, hierarchical models and spatial point processes, but does not require prior exposure Includes lavish use of figures/illustrations throughout the volume as well as analyses of several data sets (in the form of "data breaks") Exercises based on data analyses reinforce concepts

Download or read book Bayes Rules written by Alicia A. Johnson and published by CRC Press. This book was released on 2022-03-03 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.