Random Fields

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Markov Random Fields

Y.A. Rozanov
Markov Random Fields Book PDF

Author : Y.A. Rozanov
Publisher : Springer Science & Business Media
Page : 207 pages
File Size : 53,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461381907

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Markov Random Fields by Y.A. Rozanov Pdf

In this book we study Markov random functions of several variables. What is traditionally meant by the Markov property for a random process (a random function of one time variable) is connected to the concept of the phase state of the process and refers to the independence of the behavior of the process in the future from its behavior in the past, given knowledge of its state at the present moment. Extension to a generalized random process immediately raises nontrivial questions about the definition of a suitable" phase state," so that given the state, future behavior does not depend on past behavior. Attempts to translate the Markov property to random functions of multi-dimensional "time," where the role of "past" and "future" are taken by arbitrary complementary regions in an appro priate multi-dimensional time domain have, until comparatively recently, been carried out only in the framework of isolated examples. How the Markov property should be formulated for generalized random functions of several variables is the principal question in this book. We think that it has been substantially answered by recent results establishing the Markov property for a whole collection of different classes of random functions. These results are interesting for their applications as well as for the theory. In establishing them, we found it useful to introduce a general probability model which we have called a random field. In this book we investigate random fields on continuous time domains. Contents CHAPTER 1 General Facts About Probability Distributions §1.

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 : 52,6 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

Random Fields and Geometry

R. J. Adler,Jonathan E. Taylor
Random Fields and Geometry Book PDF

Author : R. J. Adler,Jonathan E. Taylor
Publisher : Springer Science & Business Media
Page : 455 pages
File Size : 43,5 Mb
Release : 2009-01-29
Category : Mathematics
ISBN : 9780387481166

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Random Fields and Geometry by R. J. Adler,Jonathan E. Taylor Pdf

This monograph is devoted to a completely new approach to geometric problems arising in the study of random fields. The groundbreaking material in Part III, for which the background is carefully prepared in Parts I and II, is of both theoretical and practical importance, and striking in the way in which problems arising in geometry and probability are beautifully intertwined. "Random Fields and Geometry" will be useful for probabilists and statisticians, and for theoretical and applied mathematicians who wish to learn about new relationships between geometry and probability. It will be helpful for graduate students in a classroom setting, or for self-study. Finally, this text will serve as a basic reference for all those interested in the companion volume of the applications of the theory.

The Geometry of Random Fields

Robert J. Adler
The Geometry of Random Fields Book PDF

Author : Robert J. Adler
Publisher : SIAM
Page : 295 pages
File Size : 41,9 Mb
Release : 2010-01-28
Category : Mathematics
ISBN : 9780898716931

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The Geometry of Random Fields by Robert J. Adler Pdf

An important treatment of the geometric properties of sets generated by random fields, including a comprehensive treatment of the mathematical basics of random fields in general. It is a standard reference for all researchers with an interest in random fields, whether they be theoreticians or come from applied areas.

Spatiotemporal Random Fields

George Christakos
Spatiotemporal Random Fields Book PDF

Author : George Christakos
Publisher : Elsevier
Page : 696 pages
File Size : 42,6 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

Markov Random Fields for Vision and Image Processing

Andrew Blake,Pushmeet Kohli,Carsten Rother
Markov Random Fields for Vision and Image Processing Book PDF

Author : Andrew Blake,Pushmeet Kohli,Carsten Rother
Publisher : MIT Press
Page : 472 pages
File Size : 50,6 Mb
Release : 2011-07-22
Category : Computers
ISBN : 9780262297448

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Markov Random Fields for Vision and Image Processing by Andrew Blake,Pushmeet Kohli,Carsten Rother Pdf

State-of-the-art research on MRFs, successful MRF applications, and advanced topics for future study. This volume demonstrates the power of the Markov random field (MRF) in vision, treating the MRF both as a tool for modeling image data and, utilizing recently developed algorithms, as a means of making inferences about images. These inferences concern underlying image and scene structure as well as solutions to such problems as image reconstruction, image segmentation, 3D vision, and object labeling. It offers key findings and state-of-the-art research on both algorithms and applications. After an introduction to the fundamental concepts used in MRFs, the book reviews some of the main algorithms for performing inference with MRFs; presents successful applications of MRFs, including segmentation, super-resolution, and image restoration, along with a comparison of various optimization methods; discusses advanced algorithmic topics; addresses limitations of the strong locality assumptions in the MRFs discussed in earlier chapters; and showcases applications that use MRFs in more complex ways, as components in bigger systems or with multiterm energy functions. The book will be an essential guide to current research on these powerful mathematical tools.

Random Fields and Spin Glasses

Cirano De Dominicis,Irene Giardina
Random Fields and Spin Glasses Book PDF

Author : Cirano De Dominicis,Irene Giardina
Publisher : Cambridge University Press
Page : 240 pages
File Size : 40,5 Mb
Release : 2006-10-26
Category : Science
ISBN : 0521847834

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Random Fields and Spin Glasses by Cirano De Dominicis,Irene Giardina Pdf

The book introduces some useful and little known techniques in statistical mechanics and field theory including multiple Legendre transforms, supersymmetry, Fourier transforms on a tree, infinitesimal permutations and Ward Takahashi Identities."--Jacket.

Stationary Sequences and Random Fields

Murray Rosenblatt
Stationary Sequences and Random Fields Book PDF

Author : Murray Rosenblatt
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461251569

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Stationary Sequences and Random Fields by Murray Rosenblatt Pdf

This book has a dual purpose. One of these is to present material which selec tively will be appropriate for a quarter or semester course in time series analysis and which will cover both the finite parameter and spectral approach. The second object is the presentation of topics of current research interest and some open questions. I mention these now. In particular, there is a discussion in Chapter III of the types of limit theorems that will imply asymptotic nor mality for covariance estimates and smoothings of the periodogram. This dis cussion allows one to get results on the asymptotic distribution of finite para meter estimates that are broader than those usually given in the literature in Chapter IV. A derivation of the asymptotic distribution for spectral (second order) estimates is given under an assumption of strong mixing in Chapter V. A discussion of higher order cumulant spectra and their large sample properties under appropriate moment conditions follows in Chapter VI. Probability density, conditional probability density and regression estimates are considered in Chapter VII under conditions of short range dependence. Chapter VIII deals with a number of topics. At first estimates for the structure function of a large class of non-Gaussian linear processes are constructed. One can determine much more about this structure or transfer function in the non-Gaussian case than one can for Gaussian processes. In particular, one can determine almost all the phase information.

Random Fields and Stochastic Partial Differential Equations

Y. Rozanov
Random Fields and Stochastic Partial Differential Equations Book PDF

Author : Y. Rozanov
Publisher : Springer Science & Business Media
Page : 236 pages
File Size : 48,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401728386

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Random Fields and Stochastic Partial Differential Equations by Y. Rozanov Pdf

This book considers some models described by means of partial dif ferential equations and boundary conditions with chaotic stochastic disturbance. In a framework of stochastic Partial Differential Equa tions an approach is suggested to generalize solutions of stochastic Boundary Problems. The main topic concerns probabilistic aspects with applications to well-known Random Fields models which are representative for the corresponding stochastic Sobolev spaces. {The term "stochastic" in general indicates involvement of appropriate random elements. ) It assumes certain knowledge in general Analysis and Probability {Hilbert space methods, Schwartz distributions, Fourier transform) . I A very general description of the main problems considered can be given as follows. Suppose, we are considering a random field ~ in a region T ~ Rd which is associated with a chaotic (stochastic) source"' by means of the differential equation (*) in T. A typical chaotic source can be represented by an appropri ate random field"' with independent values, i. e. , generalized random function"' = ( cp, 'TJ), cp E C~(T), with independent random variables ( cp, 'fJ) for any test functions cp with disjoint supports. The property of having independent values implies a certain "roughness" of the ran dom field "' which can only be treated functionally as a very irregular Schwarz distribution. With the lack of a proper development of non linear analyses for generalized functions, let us limit ourselves to the 1 For related material see, for example, J. L. Lions, E.

An Innovation Approach to Random Fields

Takeyuki Hida,Si Si
An Innovation Approach to Random Fields Book PDF

Author : Takeyuki Hida,Si Si
Publisher : World Scientific
Page : 216 pages
File Size : 47,7 Mb
Release : 2004
Category : Mathematics
ISBN : 9812565388

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An Innovation Approach to Random Fields by Takeyuki Hida,Si Si Pdf

A random field is a mathematical model of evolutional fluctuatingcomplex systems parametrized by a multi-dimensional manifold like acurve or a surface. As the parameter varies, the random field carriesmuch information and hence it has complex stochastic structure.The authors of this book use an approach that is characteristic: namely, they first construct innovation, which is the most elementalstochastic process with a basic and simple way of dependence, and thenexpress the given field as a function of the innovation. Theytherefore establish an infinite-dimensional stochastic calculus, inparticular a stochastic variational calculus. The analysis offunctions of the innovation is essentially infinite-dimensional. Theauthors use not only the theory of functional analysis, but also theirnew tools for the study

Multiparameter Processes

Davar Khoshnevisan
Multiparameter Processes Book PDF

Author : Davar Khoshnevisan
Publisher : Springer Science & Business Media
Page : 590 pages
File Size : 50,6 Mb
Release : 2006-04-10
Category : Mathematics
ISBN : 9780387216317

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Multiparameter Processes by Davar Khoshnevisan Pdf

Self-contained presentation: from elementary material to state-of-the-art research; Much of the theory in book-form for the first time; Connections are made between probability and other areas of mathematics, engineering and mathematical physics

Random Fields

Erik Vanmarcke
Random Fields Book PDF

Author : Erik Vanmarcke
Publisher : World Scientific Publishing Company
Page : 364 pages
File Size : 52,9 Mb
Release : 2010-07-21
Category : Mathematics
ISBN : 9789813101999

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Random Fields by Erik Vanmarcke Pdf

Random variation is a fact of life that provides substance to a wide range of problems in the sciences, engineering, and economics. There is a growing need in diverse disciplines to model complex patterns of variation and interdependence using random fields, as both deterministic treatment and conventional statistics are often insufficient. An ideal random field model will capture key features of complex random phenomena in terms of a minimum number of physically meaningful and experimentally accessible parameters. This volume, a revised and expanded edition of an acclaimed book first published by the M I T Press, offers a synthesis of methods to describe and analyze and, where appropriate, predict and control random fields. There is much new material, covering both theory and applications, notably on a class of probability distributions derived from quantum mechanics, relevant to stochastic modeling in fields such as cosmology, biology and system reliability, and on discrete-unit or agent-based random processes. Random Fields is self-contained and unified in presentation. The first edition was found, in a review in EOS (American Geophysical Union) to be “both technically interesting and a pleasure to read … the presentation is clear and the book should be useful to almost anyone who uses random processes to solve problems in engineering or science … and (there is) continued emphasis on describing the mathematics in physical terms.”

Image Analysis, Random Fields and Dynamic Monte Carlo Methods

Gerhard Winkler
Image Analysis Random Fields and Dynamic Monte Carlo Methods Book PDF

Author : Gerhard Winkler
Publisher : Springer Science & Business Media
Page : 321 pages
File Size : 54,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642975226

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Image Analysis, Random Fields and Dynamic Monte Carlo Methods by Gerhard Winkler Pdf

This text is concerned with a probabilistic approach to image analysis as initiated by U. GRENANDER, D. and S. GEMAN, B.R. HUNT and many others, and developed and popularized by D. and S. GEMAN in a paper from 1984. It formally adopts the Bayesian paradigm and therefore is referred to as 'Bayesian Image Analysis'. There has been considerable and still growing interest in prior models and, in particular, in discrete Markov random field methods. Whereas image analysis is replete with ad hoc techniques, Bayesian image analysis provides a general framework encompassing various problems from imaging. Among those are such 'classical' applications like restoration, edge detection, texture discrimination, motion analysis and tomographic reconstruction. The subject is rapidly developing and in the near future is likely to deal with high-level applications like object recognition. Fascinating experiments by Y. CHOW, U. GRENANDER and D.M. KEENAN (1987), (1990) strongly support this belief.

Random Field Models in Earth Sciences

George Christakos
Random Field Models in Earth Sciences Book PDF

Author : George Christakos
Publisher : Elsevier
Page : 474 pages
File Size : 44,8 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

Markov Random Fields

Rama Chellappa,Anil K. Jain
Markov Random Fields Book PDF

Author : Rama Chellappa,Anil K. Jain
Publisher : Unknown
Page : 608 pages
File Size : 52,6 Mb
Release : 1993
Category : Mathematics
ISBN : UOM:39015029555748

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Markov Random Fields by Rama Chellappa,Anil K. Jain Pdf

Introduces the theory and application of Markov random fields in image processing/computer vision. Modelling images through the local interaction of Markov models produces algorithms for use in texture analysis, image synthesis, restoration, segmentation and surface reconstruction.