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K Differenced Vector Random Fields
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Book Synopsis K-differenced Vector Random Fields by : Rehab Alsultan
Download or read book K-differenced Vector Random Fields written by Rehab Alsultan and published by . This book was released on 2015 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is a great demand for analyzing multivariate measurements observed across space and over time, due to an increasing wealth of multivariate spatial, temporal, or spatio-temporal data, which may be treated as the realizations of vector (multivariate) random fields. As one of the most important random fields in theory and application, Gaussian random field has been extensively investigated in the literature. Non-Gaussian models and random fields are often encountered in many natural and applied science areas, with specific reasons for assuming particular non-Gaussian finite-dimensional distributions in practice. One of the objectives of this dissertation is to introduce a new non-Gaussian vector random field, which belongs to the family of elliptically contoured vector random fields. This new field is named the K-differenced vector random fields, because its finite-dimensional densities are the difference of two Bessel K functions. A K-differenced vector random field is of second-order and allows for any possible correlation structure, just as a Gaussian one does. It includes a Laplace vector random field as a limiting case. This dissertation studies the properties of the K-differenced vector random field and proposes some covariance matrix structures for not only a K-differenced vector random field but also a second-order elliptically contoured one. Other objectives of this dissertation are to construct the K-differenced random variable or random vector as the scale mixture of normal random variables or vectors and to derive its density and characteristic functions. Simulations of the K-differenced distribution have been made through Monte Carlo procedures. Maximum likelihood estimators of the parameters for the simulations are found numerically via MatLab.
Book Synopsis Image Textures and Gibbs Random Fields by : Georgy L. Gimel'farb
Download or read book Image Textures and Gibbs Random Fields written by Georgy L. Gimel'farb 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: Image analysis is one of the most challenging areas in today's computer sci ence, and image technologies are used in a host of applications. This book concentrates on image textures and presents novel techniques for their sim ulation, retrieval, and segmentation using specific Gibbs random fields with multiple pairwise interaction between signals as probabilistic image models. These models and techniques were developed mainly during the previous five years (in relation to April 1999 when these words were written). While scanning these pages you may notice that, in spite of long equa tions, the mathematical background is extremely simple. I have tried to avoid complex abstract constructions and give explicit physical (to be spe cific, "image-based") explanations to all the mathematical notions involved. Therefore it is hoped that the book can be easily read both by professionals and graduate students in computer science and electrical engineering who take an interest in image analysis and synthesis. Perhaps, mathematicians studying applications of random fields may find here some less traditional, and thus controversial, views and techniques.
Book Synopsis Stationary Sequences and Random Fields by : Murray Rosenblatt
Download or read book Stationary Sequences and Random Fields written by Murray Rosenblatt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 Stochastic Geometry, Spatial Statistics and Random Fields by : Evgeny Spodarev
Download or read book Stochastic Geometry, Spatial Statistics and Random Fields written by Evgeny Spodarev and published by Springer. This book was released on 2013-02-11 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a modern introduction to stochastic geometry, random fields and spatial statistics at a (post)graduate level. It is focused on asymptotic methods in geometric probability including weak and strong limit theorems for random spatial structures (point processes, sets, graphs, fields) with applications to statistics. Written as a contributed volume of lecture notes, it will be useful not only for students but also for lecturers and researchers interested in geometric probability and related subjects.
Book Synopsis Stochastic Differential and Difference Equations by : Imre Csiszar
Download or read book Stochastic Differential and Difference Equations written by Imre Csiszar and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 175 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 Random Fields of Piezoelectricity and Piezomagnetism by : Anatoliy Malyarenko
Download or read book Random Fields of Piezoelectricity and Piezomagnetism written by Anatoliy Malyarenko and published by Springer Nature. This book was released on 2020-11-05 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random fields are a necessity when formulating stochastic continuum theories. In this book, a theory of random piezoelectric and piezomagnetic materials is developed. First, elements of the continuum mechanics of electromagnetic solids are presented. Then the relevant linear governing equations are introduced, written in terms of either a displacement approach or a stress approach, along with linear variational principles. On this basis, a statistical description of second-order (statistically) homogeneous and isotropic rank-3 tensor-valued random fields is given. With a group-theoretic foundation, correlation functions and their spectral counterparts are obtained in terms of stochastic integrals with respect to certain random measures for the fields that belong to orthotropic, tetragonal, and cubic crystal systems. The target audience will primarily comprise researchers and graduate students in theoretical mechanics, statistical physics, and probability.
Book Synopsis Optical Coherence and Quantum Optics by : Leonard Mandel
Download or read book Optical Coherence and Quantum Optics written by Leonard Mandel and published by Cambridge University Press. This book was released on 1995-09-29 with total page 1200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic account of optical coherence theory within the framework of classical optics, as applied to such topics as radiation from sources of different states of coherence, foundations of radiometry, effects of source coherence on the spectra of radiated fields, coherence theory of laser modes, and scattering of partially coherent light by random media.
Book Synopsis Nonlinear Methods of Spectral Analysis by : S. Haykin
Download or read book Nonlinear Methods of Spectral Analysis written by S. Haykin and published by Springer Science & Business Media. This book was released on 2006-01-21 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: With contributions by numerous experts
Book Synopsis Advances in Cryptology - EUROCRYPT 2007 by : Moni Naor
Download or read book Advances in Cryptology - EUROCRYPT 2007 written by Moni Naor and published by Springer Science & Business Media. This book was released on 2007-05-09 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation This book constitutes the refereed proceedings of the 26th Annual International Conference on the Theory and Applications of Cryptographic Techniques, EUROCRYPT 2007, held in Barcelona, Spain in May 2007. The 33 revised full papers presented were carefully reviewed and selected from 173 submissions. The papers address all current foundational, theoretical and research aspects of cryptology, cryptography, and cryptanalysis as well as advanced applications.
Book Synopsis Stochastic Modeling of Microstructures by : Kazimierz Sobczyk
Download or read book Stochastic Modeling of Microstructures written by Kazimierz Sobczyk and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is for a general scientific and engineering audience as a guide to current ideas, methods, and models for stochastic modeling of microstructures. It is a reference for professionals in material modeling, mechanical engineering, materials science, chemical, civil, environmental engineering and applied mathematics.
Book Synopsis Mathematical Problems and Methods of Hydrodynamic Weather Forecasting by : Vladimir Gordin
Download or read book Mathematical Problems and Methods of Hydrodynamic Weather Forecasting written by Vladimir Gordin and published by CRC Press. This book was released on 2000-09-20 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material provides an historical background to forecasting developments as well as introducing recent advances. The book will be of interest to both mathematicians and physicians, the topics covered include equations of dynamical meteorology, first integrals, non-linear stability, well-posedness of boundary problems, non-smooth solutions, parame
Book Synopsis Advanced Signal Analysis with Applications by : Harish Parthasarathy
Download or read book Advanced Signal Analysis with Applications written by Harish Parthasarathy and published by I K International Pvt Ltd. This book was released on 2011-04-01 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a sequel to the two previous books on signal analysis applications. The book applies the standard tools of signal analysis like differential calculus, probability theory, mechanism processes, partial differential equations, group theory and linear algebra to a variety of problems in physics and engineering that arise in practical applications. The book is a blend of theory and practices. In some problems, a new theoretical method is developed and in some others a well known theoretical method is applied to a new practical problem. The book will be of interest to theoretical and experimental physicists, engineers and applied mathematicians. Research students of applied mathematics and engineering will find the book extremely useful for providing new suggestions for existing problems and also for suggesting new research problems in their fields.
Book Synopsis Random Fields and Stochastic Lagrangian Models by : Karl K. Sabelfeld
Download or read book Random Fields and Stochastic Lagrangian Models written by Karl K. Sabelfeld and published by Walter de Gruyter. This book was released on 2012-12-06 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents advanced stochastic models and simulation methods for random flows and transport of particles by turbulent velocity fields and flows in porous media. Two main classes of models are constructed: (1) turbulent flows are modeled as synthetic random fields which have certain statistics and features mimicing those of turbulent fluid in the regime of interest, and (2) the models are constructed in the form of stochastic differential equations for stochastic Lagrangian trajectories of particles carried by turbulent flows. The book is written for mathematicians, physicists, and engineers studying processes associated with probabilistic interpretation, researchers in applied and computational mathematics, in environmental and engineering sciences dealing with turbulent transport and flows in porous media, as well as nucleation, coagulation, and chemical reaction analysis under fluctuation conditions. It can be of interest for students and post-graduates studying numerical methods for solving stochastic boundary value problems of mathematical physics and dispersion of particles by turbulent flows and flows in porous media.
Book Synopsis Random Fields and Geometry by : R. J. Adler
Download or read book Random Fields and Geometry written by R. J. Adler and published by Springer Science & Business Media. This book was released on 2009-01-29 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Journal of Research of the National Bureau of Standards by : United States. National Bureau of Standards
Download or read book Journal of Research of the National Bureau of Standards written by United States. National Bureau of Standards and published by . This book was released on 1960 with total page 832 pages. Available in PDF, EPUB and Kindle. Book excerpt:
