Download or read book A Review of Gaussian Random Fields and Correlation Functions written by Petter Abrahamsen and published by . This book was released on 1997 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.?
Download or read book Lectures on Probability and Second Order Random Fields written by Diego Bricio Hern ndez and published by World Scientific. This book was released on 1995 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book of lecture notes contains theoretical background material required for computer generation of random fields, which is of interest in various fields of applied mathematics.The necessary probabilistic background suitable for applied work in engineering as well as signal and image processing is also covered.The book is a valuable guide for higher level engineering students.
Download or read book Correlation Theory of Stationary and Related Random Functions written by A.M. Yaglom and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Correlation Theory of Stationary and Related Random Functions is an elementary introduction to the most important part of the theory dealing only with the first and second moments of these functions. This theory is a significant part of modern probability theory and offers both intrinsic mathematical interest and many concrete and practical applications. Stationary random functions arise in connection with stationary time series which are so important in many areas of engineering and other applications. This book presents the theory in such a way that it can be understood by readers without specialized mathematical backgrounds, requiring only the knowledge of elementary calculus. The first volume in this two-volume exposition contains the main theory; the supplementary notes and references of the second volume consist of detailed discussions of more specialized questions, some more additional material (which assumes a more thorough mathematical background than the rest of the book) and numerous references to the extensive literature.
Download or read book The Geometry of Random Fields written by Robert J. Adler and published by SIAM. This book was released on 2010-01-28 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Download or read book Handbook of Design and Analysis of Experiments written by Angela Dean and published by CRC Press. This book was released on 2015-06-26 with total page 946 pages. Available in PDF, EPUB and Kindle. Book excerpt: This carefully edited collection synthesizes the state of the art in the theory and applications of designed experiments and their analyses. It provides a detailed overview of the tools required for the optimal design of experiments and their analyses. The handbook covers many recent advances in the field, including designs for nonlinear models and algorithms applicable to a wide variety of design problems. It also explores the extensive use of experimental designs in marketing, the pharmaceutical industry, engineering and other areas.
Download or read book Gaussian Process Regression Analysis for Functional Data written by Jian Qing Shi and published by CRC Press. This book was released on 2011-07-01 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gaussian Process Regression Analysis for Functional Data presents nonparametric statistical methods for functional regression analysis, specifically the methods based on a Gaussian process prior in a functional space. The authors focus on problems involving functional response variables and mixed covariates of functional and scalar variables. Covering the basics of Gaussian process regression, the first several chapters discuss functional data analysis, theoretical aspects based on the asymptotic properties of Gaussian process regression models, and new methodological developments for high dimensional data and variable selection. The remainder of the text explores advanced topics of functional regression analysis, including novel nonparametric statistical methods for curve prediction, curve clustering, functional ANOVA, and functional regression analysis of batch data, repeated curves, and non-Gaussian data. Many flexible models based on Gaussian processes provide efficient ways of model learning, interpreting model structure, and carrying out inference, particularly when dealing with large dimensional functional data. This book shows how to use these Gaussian process regression models in the analysis of functional data. Some MATLAB® and C codes are available on the first author’s website.
Download or read book Data Analysis in Cosmology written by Vicent J. Martinez and published by Springer Science & Business Media. This book was released on 2009-03-15 with total page 636 pages. Available in PDF, EPUB and Kindle. Book excerpt: The amount of cosmological data has dramatically increased in the past decades due to an unprecedented development of telescopes, detectors and satellites. Efficiently handling and analysing new data of the order of terabytes per day requires not only computer power to be processed but also the development of sophisticated algorithms and pipelines. Aiming at students and researchers the lecture notes in this volume explain in pedagogical manner the best techniques used to extract information from cosmological data, as well as reliable methods that should help us improve our view of the universe.
Download or read book Bayesian Statistics 9 written by José M. Bernardo and published by Oxford University Press. This book was released on 2011-10-06 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian statistics is a dynamic and fast-growing area of statistical research and the Valencia International Meetings provide the main forum for discussion. These resulting proceedings form an up-to-date collection of research.
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.
Download or read book Analytical Methods in Petroleum Upstream Applications written by Cesar Ovalles and published by CRC Press. This book was released on 2015-04-02 with total page 1351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Effective measurement of the composition and properties of petroleum is essential for its exploration, production, and refining; however, new technologies and methodologies are not adequately documented in much of the current literature. Analytical Methods in Petroleum Upstream Applications explores advances in the analytical methods and instrumentation that allow more accurate determination of the components, classes of compounds, properties, and features of petroleum and its fractions. Recognized experts explore a host of topics, including: A petroleum molecular composition continuity model as a context for other analytical measurements A modern modular sampling system for use in the lab or the process area to collect and control samples for subsequent analysis The importance of oil-in-water measurements and monitoring The chemical and physical properties of heavy oils, their fractions, and products from their upgrading Analytical measurements using gas chromatography and nuclear magnetic resonance (NMR) applications Asphaltene and heavy ends analysis Chemometrics and modeling approaches for understanding petroleum composition and properties to improve upstream, midstream, and downstream operations Due to the renaissance of gas and oil production in North America, interest has grown in analytical methods for a wide range of applications. The understanding provided in this text is designed to help chemists, geologists, and chemical and petroleum engineers make more accurate estimates of the crude value to specific refinery configurations, providing insight into optimum development and extraction schemes.
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 Neuromathematics of Vision written by Giovanna Citti and published by Springer Science & Business Media. This book was released on 2014-02-08 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of the functional architecture of the visual cortex. Its geometrical structure is the differential geometry of the connectivity between neural cells. This connectivity is building and shaping the hidden brain structures underlying visual perception. The story of the problem runs over the last 30 years, since the discovery of Hubel and Wiesel of the modular structure of the primary visual cortex, and slowly cams towards a theoretical understanding of the experimental data on what we now know as functional architecture of the primary visual cortex. Experimental data comes from several domains: neurophysiology, phenomenology of perception and neurocognitive imaging. Imaging techniques like functional MRI and diffusion tensor MRI allow to deepen the study of cortical structures. Due to this variety of experimental data, neuromathematematics deals with modelling both cortical structures and perceptual spaces. From the mathematical point of view, neuromathematical call for new instruments of pure mathematics: sub-Riemannian geometry models horizontal connectivity, harmonic analysis in non commutative groups allows to understand pinwheels structure, as well as non-linear dimensionality reduction is at the base of many neural morphologies and possibly of the emergence of perceptual units. But at the center of the neurogeometry is the problem of harmonizing contemporary mathematical instruments with neurophysiological findings and phenomenological experiments in an unitary science of vision. The contributions to this book come from the very founders of the discipline.
Download or read book Information Theory Inference and Learning Algorithms written by David J. C. MacKay and published by Cambridge University Press. This book was released on 2003-09-25 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: Information theory and inference, taught together in this exciting textbook, lie at the heart of many important areas of modern technology - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics and cryptography. The book introduces theory in tandem with applications. Information theory is taught alongside practical communication systems such as arithmetic coding for data compression and sparse-graph codes for error-correction. Inference techniques, including message-passing algorithms, Monte Carlo methods and variational approximations, are developed alongside applications to clustering, convolutional codes, independent component analysis, and neural networks. Uniquely, the book covers state-of-the-art error-correcting codes, including low-density-parity-check codes, turbo codes, and digital fountain codes - the twenty-first-century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, the book is ideal for self-learning, and for undergraduate or graduate courses. It also provides an unparalleled entry point for professionals in areas as diverse as computational biology, financial engineering and machine learning.
Download or read book Large Scale Inverse Problems and Quantification of Uncertainty written by Lorenz Biegler and published by John Wiley & Sons. This book was released on 2011-06-24 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on computational methods for large-scale statistical inverse problems and provides an introduction to statistical Bayesian and frequentist methodologies. Recent research advances for approximation methods are discussed, along with Kalman filtering methods and optimization-based approaches to solving inverse problems. The aim is to cross-fertilize the perspectives of researchers in the areas of data assimilation, statistics, large-scale optimization, applied and computational mathematics, high performance computing, and cutting-edge applications. The solution to large-scale inverse problems critically depends on methods to reduce computational cost. Recent research approaches tackle this challenge in a variety of different ways. Many of the computational frameworks highlighted in this book build upon state-of-the-art methods for simulation of the forward problem, such as, fast Partial Differential Equation (PDE) solvers, reduced-order models and emulators of the forward problem, stochastic spectral approximations, and ensemble-based approximations, as well as exploiting the machinery for large-scale deterministic optimization through adjoint and other sensitivity analysis methods. Key Features: Brings together the perspectives of researchers in areas of inverse problems and data assimilation. Assesses the current state-of-the-art and identify needs and opportunities for future research. Focuses on the computational methods used to analyze and simulate inverse problems. Written by leading experts of inverse problems and uncertainty quantification. Graduate students and researchers working in statistics, mathematics and engineering will benefit from this book.
Download or read book Bayesian Time Series Models written by David Barber and published by Cambridge University Press. This book was released on 2011-08-11 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first unified treatment of time series modelling techniques spanning machine learning, statistics, engineering and computer science.
