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Author: Sujit Sahu Publisher: CRC Press ISBN: 1000543692 Category : Mathematics Languages : en Pages : 385
Book Description
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.
Author: Sujit Sahu Publisher: CRC Press ISBN: 1000543692 Category : Mathematics Languages : en Pages : 385
Book Description
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.
Author: Anthony O' Hagan Publisher: OUP Oxford ISBN: 0191613894 Category : Mathematics Languages : en Pages : 924
Book Description
Bayesian analysis has developed rapidly in applications in the last two decades and research in Bayesian methods remains dynamic and fast-growing. Dramatic advances in modelling concepts and computational technologies now enable routine application of Bayesian analysis using increasingly realistic stochastic models, and this drives the adoption of Bayesian approaches in many areas of science, technology, commerce, and industry. This Handbook explores contemporary Bayesian analysis across a variety of application areas. Chapters written by leading exponents of applied Bayesian analysis showcase the scientific ease and natural application of Bayesian modelling, and present solutions to real, engaging, societally important and demanding problems. The chapters are grouped into five general areas: Biomedical & Health Sciences; Industry, Economics & Finance; Environment & Ecology; Policy, Political & Social Sciences; and Natural & Engineering Sciences, and Appendix material in each touches on key concepts, models, and techniques of the chapter that are also of broader pedagogic and applied interest.
Author: Elias T. Krainski Publisher: CRC Press ISBN: 0429629850 Category : Mathematics Languages : en Pages : 284
Book Description
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.
Author: Christopher K. Wikle Publisher: CRC Press ISBN: 0429649789 Category : Mathematics Languages : en Pages : 397
Book Description
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.
Author: Robert P. Haining Publisher: CRC Press ISBN: 0429529104 Category : Mathematics Languages : en Pages : 556
Book Description
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.
Author: David Insua Publisher: John Wiley & Sons ISBN: 1118304039 Category : Mathematics Languages : en Pages : 315
Book Description
Bayesian analysis of complex models based on stochastic processes has in recent years become a growing area. This book provides a unified treatment of Bayesian analysis of models based on stochastic processes, covering the main classes of stochastic processing including modeling, computational, inference, forecasting, decision making and important applied models. Key features: Explores Bayesian analysis of models based on stochastic processes, providing a unified treatment. Provides a thorough introduction for research students. Computational tools to deal with complex problems are illustrated along with real life case studies Looks at inference, prediction and decision making. Researchers, graduate and advanced undergraduate students interested in stochastic processes in fields such as statistics, operations research (OR), engineering, finance, economics, computer science and Bayesian analysis will benefit from reading this book. With numerous applications included, practitioners of OR, stochastic modelling and applied statistics will also find this book useful.
Author: Birgir Hrafnkelsson Publisher: Springer Nature ISBN: 3031397916 Category : Mathematics Languages : en Pages : 256
Book Description
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.
Author: Simo Särkkä Publisher: Cambridge University Press ISBN: 110703065X Category : Computers Languages : en Pages : 255
Book Description
A unified Bayesian treatment of the state-of-the-art filtering, smoothing, and parameter estimation algorithms for non-linear state space models.
Author: Marc G. Genton Publisher: CRC Press ISBN: 0203492005 Category : Mathematics Languages : en Pages : 420
Book Description
This book reviews the state-of-the-art advances in skew-elliptical distributions and provides many new developments in a single volume, collecting theoretical results and applications previously scattered throughout the literature. The main goal of this research area is to develop flexible parametric classes of distributions beyond the classical no
Author: J.K. Ghosh Publisher: Springer Science & Business Media ISBN: 0387226540 Category : Mathematics Languages : en Pages : 311
Book Description
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.
Author: Sujit Sahu
Author: Sujit Sahu
Author: Anthony O' Hagan
Author: Elias T. Krainski
Author: Christopher K. Wikle
Author: Robert P. Haining
Author: David Insua
Author: Birgir Hrafnkelsson
Author: Simo Särkkä
Author: Marc G. Genton
Author: J.K. Ghosh