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Maximum Likelihood Estimation Of Covariance Parameters For Gaussian Random Fields
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Book Synopsis Covariance Modeling and Parameter Estimation for Stationary Spatio-temporal Gaussian Random Fields by : Benjamin Adam Shaby
Download or read book Covariance Modeling and Parameter Estimation for Stationary Spatio-temporal Gaussian Random Fields written by Benjamin Adam Shaby and published by . This book was released on 2007 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Random Fields for Spatial Data Modeling by : Dionissios T. Hristopulos
Download or read book Random Fields for Spatial Data Modeling written by Dionissios T. Hristopulos and published by Springer Nature. This book was released on 2020-02-17 with total page 884 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Gaussian Random Processes by : I.A. Ibragimov
Download or read book Gaussian Random Processes written by I.A. Ibragimov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals mainly with three problems involving Gaussian stationary processes. The first problem consists of clarifying the conditions for mutual absolute continuity (equivalence) of probability distributions of a "random process segment" and of finding effective formulas for densities of the equiva lent distributions. Our second problem is to describe the classes of spectral measures corresponding in some sense to regular stationary processes (in par ticular, satisfying the well-known "strong mixing condition") as well as to describe the subclasses associated with "mixing rate". The third problem involves estimation of an unknown mean value of a random process, this random process being stationary except for its mean, i. e. , it is the problem of "distinguishing a signal from stationary noise". Furthermore, we give here auxiliary information (on distributions in Hilbert spaces, properties of sam ple functions, theorems on functions of a complex variable, etc. ). Since 1958 many mathematicians have studied the problem of equivalence of various infinite-dimensional Gaussian distributions (detailed and sys tematic presentation of the basic results can be found, for instance, in [23]). In this book we have considered Gaussian stationary processes and arrived, we believe, at rather definite solutions. The second problem mentioned above is closely related with problems involving ergodic theory of Gaussian dynamic systems as well as prediction theory of stationary processes.
Book Synopsis Handbook of Environmental and Ecological Statistics by : Alan E. Gelfand
Download or read book Handbook of Environmental and Ecological Statistics written by Alan E. Gelfand and published by CRC Press. This book was released on 2019-01-15 with total page 876 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook focuses on the enormous literature applying statistical methodology and modelling to environmental and ecological processes. The 21st century statistics community has become increasingly interdisciplinary, bringing a large collection of modern tools to all areas of application in environmental processes. In addition, the environmental community has substantially increased its scope of data collection including observational data, satellite-derived data, and computer model output. The resultant impact in this latter community has been substantial; no longer are simple regression and analysis of variance methods adequate. The contribution of this handbook is to assemble a state-of-the-art view of this interface. Features: An internationally regarded editorial team. A distinguished collection of contributors. A thoroughly contemporary treatment of a substantial interdisciplinary interface. Written to engage both statisticians as well as quantitative environmental researchers. 34 chapters covering methodology, ecological processes, environmental exposure, and statistical methods in climate science.
Book Synopsis Gaussian Markov Random Fields by : Havard Rue
Download or read book Gaussian Markov Random Fields written by Havard Rue and published by CRC Press. This book was released on 2005-02-18 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Interpolation of Spatial Data by : Michael L. Stein
Download or read book Interpolation of Spatial Data written by Michael L. Stein and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: A summary of past work and a description of new approaches to thinking about kriging, commonly used in the prediction of a random field based on observations at some set of locations in mining, hydrology, atmospheric sciences, and geography.
Book Synopsis Statistical Methods for Spatial Data Analysis by : Oliver Schabenberger
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 444 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 Pattern Theory written by Ulf Grenander and published by Oxford University Press. This book was released on 2007 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pattern Theory provides a comprehensive and accessible overview of the modern challenges in signal, data, and pattern analysis in speech recognition, computational linguistics, image analysis and computer vision. Aimed at graduate students in biomedical engineering, mathematics, computer science, and electrical engineering with a good background in mathematics and probability, the text includes numerous exercises and an extensive bibliography. Additional resources including extended proofs, selected solutions and examples are available on a companion website. The book commences with a short overview of pattern theory and the basics of statistics and estimation theory. Chapters 3-6 discuss the role of representation of patterns via condition structure. Chapters 7 and 8 examine the second central component of pattern theory: groups of geometric transformation applied to the representation of geometric objects. Chapter 9 moves into probabilistic structures in the continuum, studying random processes and random fields indexed over subsets of Rn. Chapters 10 and 11 continue with transformations and patterns indexed over the continuum. Chapters 12-14 extend from the pure representations of shapes to the Bayes estimation of shapes and their parametric representation. Chapters 15 and 16 study the estimation of infinite dimensional shape in the newly emergent field of Computational Anatomy. Finally, Chapters 17 and 18 look at inference, exploring random sampling approaches for estimation of model order and parametric representing of shapes.
Book Synopsis Advances in Contemporary Statistics and Econometrics by : Abdelaati Daouia
Download or read book Advances in Contemporary Statistics and Econometrics written by Abdelaati Daouia and published by Springer Nature. This book was released on 2021-06-14 with total page 713 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unique collection of contributions on modern topics in statistics and econometrics, written by leading experts in the respective disciplines and their intersections. It addresses nonparametric statistics and econometrics, quantiles and expectiles, and advanced methods for complex data, including spatial and compositional data, as well as tools for empirical studies in economics and the social sciences. The book was written in honor of Christine Thomas-Agnan on the occasion of her 65th birthday. Given its scope, it will appeal to researchers and PhD students in statistics and econometrics alike who are interested in the latest developments in their field.
Book Synopsis Handbook of Spatial Statistics by : Alan E. Gelfand
Download or read book Handbook of Spatial Statistics written by Alan E. Gelfand and published by CRC Press. This book was released on 2010-03-19 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Value of Information in the Earth Sciences by : Jo Eidsvik
Download or read book Value of Information in the Earth Sciences written by Jo Eidsvik and published by Cambridge University Press. This book was released on 2015-11-19 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gathering the right kind and the right amount of information is crucial for any decision-making process. This book presents a unified framework for assessing the value of potential data gathering schemes by integrating spatial modelling and decision analysis, with a focus on the Earth sciences. The authors discuss the value of imperfect versus perfect information, and the value of total versus partial information, where only subsets of the data are acquired. Concepts are illustrated using a suite of quantitative tools from decision analysis, such as decision trees and influence diagrams, as well as models for continuous and discrete dependent spatial variables, including Bayesian networks, Markov random fields, Gaussian processes, and multiple-point geostatistics. Unique in scope, this book is of interest to students, researchers and industry professionals in the Earth and environmental sciences, who use applied statistics and decision analysis techniques, and particularly to those working in petroleum, mining, and environmental geoscience.
Download or read book Biometrika written by and published by . This book was released on 1992 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Data Science: Theory and Applications by :
Download or read book Data Science: Theory and Applications written by and published by Elsevier. This book was released on 2021-02-12 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Data Science: Theory and Applications, Volume 44 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters on a variety of interesting topics, including Modeling extreme climatic events using the generalized extreme value distribution, Bayesian Methods in Data Science, Mathematical Modeling in Health Economic Evaluations, Data Science in Cancer Genomics, Blockchain Technology: Theory and Practice, Statistical outline of animal home ranges, an application of set estimation, Application of Data Handling Techniques to Predict Pavement Performance, Analysis of individual treatment effects for enhanced inferences in medicine, and more. Additional sections cover Nonparametric Data Science: Testing Hypotheses in Large Complex Data, From Urban Mobility Problems to Data Science Solutions, and Data Structures and Artificial Intelligence Methods. - Provides the authority and expertise of leading contributors from an international board of authors - Presents the latest release in the Handbook of Statistics series - Updated release includes the latest information on Data Science: Theory and Applications
Book Synopsis Computational Techniques And Applications - Proceedings Of The Sixth Biennial Conference by : Henry J Gardner
Download or read book Computational Techniques And Applications - Proceedings Of The Sixth Biennial Conference written by Henry J Gardner and published by World Scientific. This book was released on 1994-06-28 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers on computational mathematics, development, implementation, and application of numerical algorithms, the development and application of computational systems, and numerical modelling. Also featured are reports on applications of advanced computer architectures and innovative visualisation techniques. It will be a help for developers and implementors of computational methods who wish to find out more about the work of those applying the technology to problems in engineering and science, and vice versa.
Book Synopsis Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science by : Isaac Pesenson
Download or read book Recent Applications of Harmonic Analysis to Function Spaces, Differential Equations, and Data Science written by Isaac Pesenson and published by Birkhäuser. This book was released on 2017-08-09 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such as: The classical Fourier transform, the non-linear Fourier transform (FBI transform), cardinal sampling series and translation invariant linear systems. Recent results concerning harmonic analysis on non-Euclidean spaces such as graphs and partially ordered sets. Applications of harmonic analysis to data science and statistics Boundary-value problems for PDE's including the Runge–Walsh theorem for the oblique derivative problem of physical geodesy.
Book Synopsis Inverse Problems in Groundwater Modeling by : Ne-Zheng Sun
Download or read book Inverse Problems in Groundwater Modeling written by Ne-Zheng Sun and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: ... A diskette with the updated programme of Appendix C and examples is available through the author at a small fee. email: [email protected] fax: 1--310--825--5435 ... This book systematically discusses basic concepts, theory, solution methods and applications of inverse problems in groundwater modeling. It is the first book devoted to this subject. The inverse problem is defined and solved in both deterministic and statistic frameworks. Various direct and indirect methods are discussed and compared. As a useful tool, the adjoint state method and its applications are given in detail. For a stochastic field, the maximum likelihood estimation and co-kriging techniques are used to estimate unknown parameters. The ill-posed problem of inverse solution is highlighted through the whole book. The importance of data collection strategy is specially emphasized. Besides the classical design criteria, the relationships between decision making, prediction, parameter identification and experimental design are considered from the point of view of extended identifiabilities. The problem of model structure identification is also considered. This book can be used as a textbook for graduate students majoring in hydrogeology or related subjects. It is also a reference book for hydrogeologists, petroleum engineers, environmental engineers, mining engineers and applied mathematicians.
Book Synopsis Long-Range Dependence and Self-Similarity by : Vladas Pipiras
Download or read book Long-Range Dependence and Self-Similarity written by Vladas Pipiras and published by Cambridge University Press. This book was released on 2017-04-18 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: This modern and comprehensive guide to long-range dependence and self-similarity starts with rigorous coverage of the basics, then moves on to cover more specialized, up-to-date topics central to current research. These topics concern, but are not limited to, physical models that give rise to long-range dependence and self-similarity; central and non-central limit theorems for long-range dependent series, and the limiting Hermite processes; fractional Brownian motion and its stochastic calculus; several celebrated decompositions of fractional Brownian motion; multidimensional models for long-range dependence and self-similarity; and maximum likelihood estimation methods for long-range dependent time series. Designed for graduate students and researchers, each chapter of the book is supplemented by numerous exercises, some designed to test the reader's understanding, while others invite the reader to consider some of the open research problems in the field today.