Random Fields For Spatial Data Modeling

Author : Dionissios T. Hristopulos
Publisher : Springer Nature
Page : 884 pages
File Size : 47,6 Mb
Release : 2020-02-17
Category : Science
ISBN : 9789402419184

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Random Fields for Spatial Data Modeling by Dionissios T. Hristopulos Pdf

This book provides an inter-disciplinary introduction to the theory of random fields and its applications. Spatial models and spatial data analysis are integral parts of many scientific and engineering disciplines. Random fields provide a general theoretical framework for the development of spatial models and their applications in data analysis. The contents of the book include topics from classical statistics and random field theory (regression models, Gaussian random fields, stationarity, correlation functions) spatial statistics (variogram estimation, model inference, kriging-based prediction) and statistical physics (fractals, Ising model, simulated annealing, maximum entropy, functional integral representations, perturbation and variational methods). The book also explores links between random fields, Gaussian processes and neural networks used in machine learning. Connections with applied mathematics are highlighted by means of models based on stochastic partial differential equations. An interlude on autoregressive time series provides useful lower-dimensional analogies and a connection with the classical linear harmonic oscillator. Other chapters focus on non-Gaussian random fields and stochastic simulation methods. The book also presents results based on the author’s research on Spartan random fields that were inspired by statistical field theories originating in physics. The equivalence of the one-dimensional Spartan random field model with the classical, linear, damped harmonic oscillator driven by white noise is highlighted. Ideas with potentially significant computational gains for the processing of big spatial data are presented and discussed. The final chapter concludes with a description of the Karhunen-Loève expansion of the Spartan model. The book will appeal to engineers, physicists, and geoscientists whose research involves spatial models or spatial data analysis. Anyone with background in probability and statistics can read at least parts of the book. Some chapters will be easier to understand by readers familiar with differential equations and Fourier transforms.

Author : Xavier Guyon
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 55,5 Mb
Release : 1995-06-23
Category : Mathematics
ISBN : 0387944281

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Random Fields on a Network by Xavier Guyon Pdf

The theory of spatial models over lattices, or random fields as they are known, has developed significantly over recent years. This book provides a graduate-level introduction to the subject which assumes only a basic knowledge of probability and statistics, finite Markov chains, and the spectral theory of second-order processes. A particular strength of this book is its emphasis on examples - both to motivate the theory which is being developed, and to demonstrate the applications which range from statistical mechanics to image analysis and from statistics to stochastic algorithms.

Author : George Christakos
Publisher : Elsevier
Page : 474 pages
File Size : 40,7 Mb
Release : 2013-10-22
Category : Science
ISBN : 9781483288307

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Random Field Models in Earth Sciences by George Christakos Pdf

This book is about modeling as a prinicipal component of scientific investigations. In general terms, modeling is the funamental process of combining intellectual creativity with physical knowledge and mathematical techniques in order to learn the properties of the mechanisms underlying a physical phenomenon and make predictions. The book focuses on a specific class of models, namely, random field models and certain of their physical applications in the context of a stochastic data analysis and processing research program. The term application is considered here in the sense wherein the mathematical random field model is shaping, but is also being shaped by, its objects. Key Features * This book explores the application of random field models and stochastic data processing to problems in hydrogeology, geostatistics, climate modeling, and oil reservoir engineering, among others Researchers in the geosciences who work with models of natural processes will find discussion of; * Spatiotemporal random fields * Space transformation * Multidimensional estimation * Simulation * Sampling design * Stochastic partial differential equations

Author : Werner G. Müller
Publisher : Springer Science & Business Media
Page : 250 pages
File Size : 44,6 Mb
Release : 2007-08-17
Category : Business & Economics
ISBN : 9783540311751

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Collecting Spatial Data by Werner G. Müller Pdf

The book is concerned with the statistical theory for locating spatial sensors. It bridges the gap between spatial statistics and optimum design theory. After introductions to those two fields the topics of exploratory designs and designs for spatial trend and variogram estimation are treated. Special attention is devoted to describing new methodologies to cope with the problem of correlated observations.

Author : Havard Rue,Leonhard Held
Publisher : CRC Press
Page : 280 pages
File Size : 40,5 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

Author : Oliver Schabenberger,Carol A. Gotway
Publisher : CRC Press
Page : 512 pages
File Size : 46,7 Mb
Release : 2017-01-27
Category : Mathematics
ISBN : 9781482258134

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Statistical Methods for Spatial Data Analysis by Oliver Schabenberger,Carol A. Gotway Pdf

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.

Author : Richard E. Plant
Publisher : CRC Press
Page : 666 pages
File Size : 50,7 Mb
Release : 2018-12-07
Category : Science
ISBN : 9781351189903

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Spatial Data Analysis in Ecology and Agriculture Using R by Richard E. Plant Pdf

Key features: Unique in its combination of serving as an introduction to spatial statistics and to modeling agricultural and ecological data using R Provides exercises in each chapter to facilitate the book's use as a course textbook or for self-study Adds new material on generalized additive models, point pattern analysis, and new methods of Bayesian analysis of spatial data. Includes a completely revised chapter on the analysis of spatiotemporal data featuring recently introduced software and methods Updates its coverage of R software including newly introduced packages Spatial Data Analysis in Ecology and Agriculture Using R, 2nd Edition provides practical instruction on the use of the R programming language to analyze spatial data arising from research in ecology, agriculture, and environmental science. Readers have praised the book's practical coverage of spatial statistics, real-world examples, and user-friendly approach in presenting and explaining R code, aspects maintained in this update. Using data sets from cultivated and uncultivated ecosystems, the book guides the reader through the analysis of each data set, including setting research objectives, designing the sampling plan, data quality control, exploratory and confirmatory data analysis, and drawing scientific conclusions. Additional material to accompany the book, on both analyzing satellite data and on multivariate analysis, can be accessed at https://www.plantsciences.ucdavis.edu/plant/additionaltopics.htm.

Author : Per Sidén
Publisher : Linköping University Electronic Press
Page : 53 pages
File Size : 41,5 Mb
Release : 2020-08-17
Category : Electronic
ISBN : 9789179298180

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Scalable Bayesian spatial analysis with Gaussian Markov random fields by Per Sidén Pdf

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.

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 : 51,7 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.

Author : Xavier Guyon
Publisher : Unknown
Page : 255 pages
File Size : 55,8 Mb
Release : 1995
Category : Random fields
ISBN : 3540944281

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Random Fields on a Network by Xavier Guyon Pdf

Author : Sudipto Banerjee,Bradley P. Carlin,Alan E. Gelfand
Publisher : CRC Press
Page : 583 pages
File Size : 54,9 Mb
Release : 2014-09-12
Category : Mathematics
ISBN : 9781439819180

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Hierarchical Modeling and Analysis for Spatial Data by Sudipto Banerjee,Bradley P. Carlin,Alan E. Gelfand Pdf

Keep Up to Date with the Evolving Landscape of Space and Space-Time Data Analysis and ModelingSince the publication of the first edition, the statistical landscape has substantially changed for analyzing space and space-time data. More than twice the size of its predecessor, Hierarchical Modeling and Analysis for Spatial Data, Second Edition reflec

Author : George Christakos
Publisher : Elsevier
Page : 696 pages
File Size : 46,8 Mb
Release : 2017-07-26
Category : Science
ISBN : 9780128030325

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Spatiotemporal Random Fields by George Christakos Pdf

Spatiotemporal Random Fields: Theory and Applications, Second Edition, provides readers with a new and updated edition of the text that explores the application of spatiotemporal random field models to problems in ocean, earth, and atmospheric sciences, spatiotemporal statistics, and geostatistics, among others. The new edition features considerable detail of spatiotemporal random field theory, including ordinary and generalized models, as well as space-time homostationary, isostationary and hetrogeneous approaches. Presenting new theoretical and applied results, with particular emphasis on space-time determination and interpretation, spatiotemporal analysis and modeling, random field geometry, random functionals, probability law, and covariance construction techniques, this book highlights the key role of space-time metrics, the physical interpretation of stochastic differential equations, higher-order space-time variability functions, the validity of major theoretical assumptions in real-world practice (covariance positive-definiteness, metric-adequacy etc.), and the emergence of interdisciplinary phenomena in conditions of multi-sourced real-world uncertainty. Contains applications in the form of examples and case studies, providing readers with first-hand experiences Presents an easy to follow narrative which progresses from simple concepts to more challenging ideas Includes significant updates from the previous edition, including a focus on new theoretical and applied results

Author : Alan E. Gelfand,Peter Diggle,Peter Guttorp,Montserrat Fuentes
Publisher : CRC Press
Page : 622 pages
File Size : 44,7 Mb
Release : 2010-03-19
Category : Mathematics
ISBN : 9781420072884

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Handbook of Spatial Statistics by Alan E. Gelfand,Peter Diggle,Peter Guttorp,Montserrat Fuentes Pdf

Assembling a collection of very prominent researchers in the field, the Handbook of Spatial Statistics presents a comprehensive treatment of both classical and state-of-the-art aspects of this maturing area. It takes a unified, integrated approach to the material, providing cross-references among chapters.The handbook begins with a historical intro

Author : Dale L. Zimmerman,Jay M. Ver Hoef
Publisher : CRC Press
Page : 400 pages
File Size : 49,9 Mb
Release : 2024-04-17
Category : Mathematics
ISBN : 9780429595097

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Spatial Linear Models for Environmental Data by Dale L. Zimmerman,Jay M. Ver Hoef Pdf

Many applied researchers equate spatial statistics with prediction or mapping, but this book naturally extends linear models, which includes regression and ANOVA as pillars of applied statistics, to achieve a more comprehensive treatment of the analysis of spatially autocorrelated data. Spatial Linear Models for Environmental Data, aimed at students and professionals with a master’s level training in statistics, presents a unique, applied, and thorough treatment of spatial linear models within a statistics framework. Two subfields, one called geostatistics and the other called areal or lattice models, are extensively covered. Zimmerman and Ver Hoef present topics clearly, using many examples and simulation studies to illustrate ideas. By mimicking their examples and R code, readers will be able to fit spatial linear models to their data and draw proper scientific conclusions. Topics covered include: Exploratory methods for spatial data including outlier detection, (semi)variograms, Moran’s I, and Geary’s c. Ordinary and generalized least squares regression methods and their application to spatial data. Suitable parametric models for the mean and covariance structure of geostatistical and areal data. Model-fitting, including inference methods for explanatory variables and likelihood-based methods for covariance parameters. Practical use of spatial linear models including prediction (kriging), spatial sampling, and spatial design of experiments for solving real world problems. All concepts are introduced in a natural order and illustrated throughout the book using four datasets. All analyses, tables, and figures are completely reproducible using open-source R code provided at a GitHub site. Exercises are given at the end of each chapter, with full solutions provided on an instructor’s FTP site supplied by the publisher.

Author : Massimo Craglia,H. Couclelis
Publisher : CRC Press
Page : 630 pages
File Size : 40,7 Mb
Release : 2020-10-28
Category : Technology & Engineering
ISBN : 9781000124064

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Geographic Information Research by Massimo Craglia,H. Couclelis Pdf

The contributors to this edited collection demonstrate that geographic information research is truly global in character, cutting across a wide range of disciplines and addressing conceptual, methodological, technical, ethical and political issues alike. Of the six themes, two are broadly concerned with data integration (geographic data infrastructures, GIS diffusion and implementation); two are more technical and conceptual in nature (generalisation, concepts and paradigms), and two reflect to a larger extent the application-driven nature of GIS technology (spatial analysis and multimedia). Each section is introduced by chapters highlighting the key research issues. Further chapters explore these issues in greater depth, and benefit from the international collaboration. Through the comparison of results included in this book, the prospects for advancing the field and addressing the challenges of GIS research are greatly improved.