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Prediction And Estimation Of Random Fields
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Book Synopsis Prediction and Estimation of Random Fields by : Priya Kohli
Download or read book Prediction and Estimation of Random Fields written by Priya Kohli and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: For a stationary two dimensional random field, we utilize the classical Kolmogorov-Wiener theory to develop prediction methodology which requires minimal assumptions on the dependence structure of the random field. We also provide solutions for several non-standard prediction problems which deals with the "modified past," in which a finite number of observations are added to the past. These non-standard prediction problems are motivated by the network site selection in the environmental and geostatistical applications. Unlike the time series situation, the prediction results for random fields seem to be expressible only in terms of the moving average parameters, and attempts to express them in terms of the autoregressive parameters lead to a new and mysterious projection operator which captures the nature of edge-effects. We put forward an approach for estimating the predictor coefficients by carrying out an extension of the exponential models. Through simulation studies and real data example, we demonstrate the impressive performance of our prediction method. To the best of our knowledge, the proposed method is the first to deliver a unified framework for forecasting random fields both in the time and spectral domain without making a subjective choice of the covariance structure. Finally, we focus on the estimation of the hurst parameter for long range dependence stationary random fields, which draws its motivation from applications in the environmental and atmospheric processes. Current methods for estimation of the Hurst parameter include parametric models like fractional autoregressive integrated moving average models, and semiparametric estimators which are either inefficient or inconsistent. We propose a novel semiparametric estimator based on the fractional exponential spectrum. We develop three data-driven methods which can automatically select the optimal model order for the fractional exponential models. Extensive simulation studies and analysis of Mercer and Hall?s wheat data are used to illustrate the performance of the proposed estimator and model order selection criteria. The results show that our estimator outperforms existing estimators, including the GPH (Geweke and Porter-Hudak) estimator. We show that the proposed estimator is consistent, works for different definitions of long range dependent random fields, is computationally simple and is not susceptible to model misspecification or poor efficiency.
Book Synopsis Multivariate Gaussian Random Fields by : Yuzhen Zhou
Download or read book Multivariate Gaussian Random Fields written by Yuzhen Zhou and published by . This book was released on 2015 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to Conditional Random Fields by : Charles Sutton
Download or read book An Introduction to Conditional Random Fields written by Charles Sutton and published by . This book was released on 2012 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many tasks involve predicting a large number of variables that depend on each other as well as on other observed variables. Structured prediction methods are essentially a combination of classification and graphical modeling. They combine the ability of graphical models to compactly model multivariate data with the ability of classification methods to perform prediction using large sets of input features. This survey describes conditional random fields, a popular probabilistic method for structured prediction. CRFs have seen wide application in many areas, including natural language processing, computer vision, and bioinformatics. We describe methods for inference and parameter estimation for CRFs, including practical issues for implementing large-scale CRFs. We do not assume previous knowledge of graphical modeling, so this survey is intended to be useful to practitioners in a wide variety of fields.
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 An Introduction to Conditional Random Fields by : Charles Sutton
Download or read book An Introduction to Conditional Random Fields written by Charles Sutton and published by Now Pub. This book was released on 2012 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Conditional Random Fields provides a comprehensive tutorial aimed at application-oriented practitioners seeking to apply CRFs. The monograph does not assume previous knowledge of graphical modeling, and so is intended to be useful to practitioners in a wide variety of fields.
Book Synopsis Collecting Spatial Data by : Werner G. Müller
Download or read book Collecting Spatial Data written by Werner G. Müller and published by Springer Science & Business Media. This book was released on 2007-08-17 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Spectral Analysis, Estimation, and Prediction of Multiple Harmonizable Random Fields and Time Series by :
Download or read book Spectral Analysis, Estimation, and Prediction of Multiple Harmonizable Random Fields and Time Series written by and published by . This book was released on 1994 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Download or read book Random Fields written by Erik Vanmarcke and published by World Scientific. This book was released on 2010 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.?
Book Synopsis Random Fields Estimation by : Alexander G. Ramm
Download or read book Random Fields Estimation written by Alexander G. Ramm and published by World Scientific. This book was released on 2005 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a novel theory of random fields estimation of Wiener type, developed originally by the author and presented here. No assumption about the Gaussian or Markovian nature of the fields are made. The theory, constructed entirely within the framework of covariance theory, is based on a detailed analytical study of a new class of multidimensional integral equations basic in estimation theory.This book is suitable for graduate courses in random fields estimation. It can also be used in courses in functional analysis, numerical analysis, integral equations, and scattering theory.
Book Synopsis Gaussian and Non-Gaussian Linear Time Series and Random Fields by : Murray Rosenblatt
Download or read book Gaussian and Non-Gaussian Linear Time Series 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 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principal focus here is on autoregressive moving average models and analogous random fields, with probabilistic and statistical questions also being discussed. The book contrasts Gaussian models with noncausal or noninvertible (nonminimum phase) non-Gaussian models and deals with problems of prediction and estimation. New results for nonminimum phase non-Gaussian processes are exposited and open questions are noted. Intended as a text for gradutes in statistics, mathematics, engineering, the natural sciences and economics, the only recommendation is an initial background in probability theory and statistics. Notes on background, history and open problems are given at the end of the book.
Book Synopsis Application of Best Linear Unbiased Prediction to Interpolation of Random Fields and to Network Design by : André Cabannes
Download or read book Application of Best Linear Unbiased Prediction to Interpolation of Random Fields and to Network Design written by André Cabannes and published by . This book was released on 1980 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt: The practical problem of monitoring air pollutant concentration over a geographical area, or of estimating the mining resources in a region or a field can both be formulated as a problem of interpolation of random field. Given a real-valued random field (Z(X), x an element of R to the m power) the basic problem is to interpolate Z over an area A from measurements taken at n stations x1,x2,.., xn, when the distribution of Z is only partially specified. The second problem is the choice of the network of stations. After deriving the form of the best linear unbiased predictor of Z we prove a general updating theorem which is useful both practically to quicken the computation of the new estimated map, and theoretically to study the problem of network design. Then we use this theorem to prove that when Z is a smooth random field (essentially differentiable in quadratic mean) the variance of estimation error of Z(x) is a discontinuous function of the arguments x1,x2, ..., xn. We discuss the practical consequences of this result in the design of networks of stations. (Author).
Book Synopsis Effective Observation of Random Fields by : Wolfgang Näther
Download or read book Effective Observation of Random Fields written by Wolfgang Näther and published by . This book was released on 1985 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Hybrid Random Fields by : Antonino Freno
Download or read book Hybrid Random Fields written by Antonino Freno and published by Springer Science & Business Media. This book was released on 2011-04-11 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an exciting new synthesis of directed and undirected, discrete and continuous graphical models. Combining elements of Bayesian networks and Markov random fields, the newly introduced hybrid random fields are an interesting approach to get the best of both these worlds, with an added promise of modularity and scalability. The authors have written an enjoyable book---rigorous in the treatment of the mathematical background, but also enlivened by interesting and original historical and philosophical perspectives. -- Manfred Jaeger, Aalborg Universitet The book not only marks an effective direction of investigation with significant experimental advances, but it is also---and perhaps primarily---a guide for the reader through an original trip in the space of probabilistic modeling. While digesting the book, one is enriched with a very open view of the field, with full of stimulating connections. [...] Everyone specifically interested in Bayesian networks and Markov random fields should not miss it. -- Marco Gori, Università degli Studi di Siena Graphical models are sometimes regarded---incorrectly---as an impractical approach to machine learning, assuming that they only work well for low-dimensional applications and discrete-valued domains. While guiding the reader through the major achievements of this research area in a technically detailed yet accessible way, the book is concerned with the presentation and thorough (mathematical and experimental) investigation of a novel paradigm for probabilistic graphical modeling, the hybrid random field. This model subsumes and extends both Bayesian networks and Markov random fields. Moreover, it comes with well-defined learning algorithms, both for discrete and continuous-valued domains, which fit the needs of real-world applications involving large-scale, high-dimensional data.
Book Synopsis Geostatistical Functional Data Analysis by : Jorge Mateu
Download or read book Geostatistical Functional Data Analysis written by Jorge Mateu and published by John Wiley & Sons. This book was released on 2021-12-13 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geostatistical Functional Data Analysis Explore the intersection between geostatistics and functional data analysis with this insightful new reference Geostatistical Functional Data Analysis presents a unified approach to modelling functional data when spatial and spatio-temporal correlations are present. The Editors link together the wide research areas of geostatistics and functional data analysis to provide the reader with a new area called geostatistical functional data analysis that will bring new insights and new open questions to researchers coming from both scientific fields. This book provides a complete and up-to-date account to deal with functional data that is spatially correlated, but also includes the most innovative developments in different open avenues in this field. Containing contributions from leading experts in the field, this practical guide provides readers with the necessary tools to employ and adapt classic statistical techniques to handle spatial regression. The book also includes: A thorough introduction to the spatial kriging methodology when working with functions A detailed exposition of more classical statistical techniques adapted to the functional case and extended to handle spatial correlations Practical discussions of ANOVA, regression, and clustering methods to explore spatial correlation in a collection of curves sampled in a region In-depth explorations of the similarities and differences between spatio-temporal data analysis and functional data analysis Aimed at mathematicians, statisticians, postgraduate students, and researchers involved in the analysis of functional and spatial data, Geostatistical Functional Data Analysis will also prove to be a powerful addition to the libraries of geoscientists, environmental scientists, and economists seeking insightful new knowledge and questions at the interface of geostatistics and functional data analysis.
Book Synopsis Random Fields Estimation Theory by : Alexander G. Ramm
Download or read book Random Fields Estimation Theory written by Alexander G. Ramm and published by Longman Scientific and Technical. This book was released on 1990 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Random Fields Estimation Theory by : Alexander G. Ramm
Download or read book Random Fields Estimation Theory written by Alexander G. Ramm and published by . This book was released on 1990 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:
