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Relative Entropy Densities Converge Almost Surely
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Book Synopsis Relative Entropy Densities Converge Almost Surely by : Stanford University. Department of Statistics
Download or read book Relative Entropy Densities Converge Almost Surely written by Stanford University. Department of Statistics and published by . This book was released on 1984 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Principles of Signal Detection and Parameter Estimation by : Bernard C. Levy
Download or read book Principles of Signal Detection and Parameter Estimation written by Bernard C. Levy and published by Springer Science & Business Media. This book was released on 2008-07-07 with total page 647 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a comprehensive and current understanding of signal detection and estimation, including problems and solutions for each chapter. Signal detection plays an important role in fields such as radar, sonar, digital communications, image processing, and failure detection. The book explores both Gaussian detection and detection of Markov chains, presenting a unified treatment of coding and modulation topics. Addresses asymptotic of tests with the theory of large deviations, and robust detection. This text is appropriate for students of Electrical Engineering in graduate courses in Signal Detection and Estimation.
Book Synopsis Entropy and Information Theory by : Robert M. Gray
Download or read book Entropy and Information Theory written by Robert M. Gray and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the theory of probabilistic information measures and their application to coding theorems for information sources and noisy channels. The eventual goal is a general development of Shannon's mathematical theory of communication, but much of the space is devoted to the tools and methods required to prove the Shannon coding theorems. These tools form an area common to ergodic theory and information theory and comprise several quantitative notions of the information in random variables, random processes, and dynamical systems. Examples are entropy, mutual information, conditional entropy, conditional information, and discrimination or relative entropy, along with the limiting normalized versions of these quantities such as entropy rate and information rate. Much of the book is concerned with their properties, especially the long term asymptotic behavior of sample information and expected information. This is the only up-to-date treatment of traditional information theory emphasizing ergodic theory.
Book Synopsis Selected Topics in Information and Coding Theory by : Isaac Woungang
Download or read book Selected Topics in Information and Coding Theory written by Isaac Woungang and published by World Scientific. This book was released on 2010 with total page 725 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last few years have witnessed rapid advancements in information and coding theory research and applications. This book provides a comprehensive guide to selected topics, both ongoing and emerging, in information and coding theory. Consisting of contributions from well-known and high-profile researchers in their respective specialties, topics that are covered include source coding; channel capacity; linear complexity; code construction, existence and analysis; bounds on codes and designs; space-time coding; LDPC codes; and codes and cryptography.All of the chapters are integrated in a manner that renders the book as a supplementary reference volume or textbook for use in both undergraduate and graduate courses on information and coding theory. As such, it will be a valuable text for students at both undergraduate and graduate levels as well as instructors, researchers, engineers, and practitioners in these fields.Supporting Powerpoint Slides are available upon request for all instructors who adopt this book as a course text.
Book Synopsis Compression-Based Methods of Statistical Analysis and Prediction of Time Series by : Boris Ryabko
Download or read book Compression-Based Methods of Statistical Analysis and Prediction of Time Series written by Boris Ryabko and published by Springer. This book was released on 2016-05-19 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Universal codes efficiently compress sequences generated by stationary and ergodic sources with unknown statistics, and they were originally designed for lossless data compression. In the meantime, it was realized that they can be used for solving important problems of prediction and statistical analysis of time series, and this book describes recent results in this area. The first chapter introduces and describes the application of universal codes to prediction and the statistical analysis of time series; the second chapter describes applications of selected statistical methods to cryptography, including attacks on block ciphers; and the third chapter describes a homogeneity test used to determine authorship of literary texts. The book will be useful for researchers and advanced students in information theory, mathematical statistics, time-series analysis, and cryptography. It is assumed that the reader has some grounding in statistics and in information theory.
Book Synopsis Relative Entropy and the Convergence of the Posteriior and Empirical 3 by :
Download or read book Relative Entropy and the Convergence of the Posteriior and Empirical 3 written by and published by . This book was released on 1988 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonparametric Econometric Methods by : Qi Li
Download or read book Nonparametric Econometric Methods written by Qi Li and published by Emerald Group Publishing. This book was released on 2009-12-04 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains a selection of papers presented initially at the 7th Annual Advances in Econometrics Conference held on the LSU campus in Baton Rouge, Louisiana during November 14-16, 2008. This work is suitable for those who wish to familiarize themselves with nonparametric methodology.
Book Synopsis Modern Multivariate Statistical Techniques by : Alan J. Izenman
Download or read book Modern Multivariate Statistical Techniques written by Alan J. Izenman and published by Springer Science & Business Media. This book was released on 2009-03-02 with total page 757 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book on multivariate analysis to look at large data sets which describes the state of the art in analyzing such data. Material such as database management systems is included that has never appeared in statistics books before.
Book Synopsis On Dobrushin's Way. From Probability Theory to Statistical Physics by : Robert A. Minlos
Download or read book On Dobrushin's Way. From Probability Theory to Statistical Physics written by Robert A. Minlos and published by American Mathematical Soc.. This book was released on 2000 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fellow Russian mathematicians discuss and extend the works of Dobrushin (1929-95,), who worked in many areas of mathematics, but had deepest influence on mathematical physics and was one of the founders of the rigorous study of statistical physics. The 15 technical papers are flanked by a short biography and recollections by colleagues and students. The topics include the lower spectral branch of the generator of the stochastic dynamics for the classical Heisenberg model, non-symmetric simple random walks along orbits of ergodic automorphisms, the Cramer transform and large deviations on three- dimensional Lobachevsky space, and dynamics of Ising-spin systems at zero temperature. No index is provided. Annotation copyrighted by Book News, Inc., Portland, OR.
Download or read book Entropy written by Andreas Greven and published by Princeton University Press. This book was released on 2014-09-08 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of entropy arose in the physical sciences during the nineteenth century, particularly in thermodynamics and statistical physics, as a measure of the equilibria and evolution of thermodynamic systems. Two main views developed: the macroscopic view formulated originally by Carnot, Clausius, Gibbs, Planck, and Caratheodory and the microscopic approach associated with Boltzmann and Maxwell. Since then both approaches have made possible deep insights into the nature and behavior of thermodynamic and other microscopically unpredictable processes. However, the mathematical tools used have later developed independently of their original physical background and have led to a plethora of methods and differing conventions. The aim of this book is to identify the unifying threads by providing surveys of the uses and concepts of entropy in diverse areas of mathematics and the physical sciences. Two major threads, emphasized throughout the book, are variational principles and Ljapunov functionals. The book starts by providing basic concepts and terminology, illustrated by examples from both the macroscopic and microscopic lines of thought. In-depth surveys covering the macroscopic, microscopic and probabilistic approaches follow. Part I gives a basic introduction from the views of thermodynamics and probability theory. Part II collects surveys that look at the macroscopic approach of continuum mechanics and physics. Part III deals with the microscopic approach exposing the role of entropy as a concept in probability theory, namely in the analysis of the large time behavior of stochastic processes and in the study of qualitative properties of models in statistical physics. Finally in Part IV applications in dynamical systems, ergodic and information theory are presented. The chapters were written to provide as cohesive an account as possible, making the book accessible to a wide range of graduate students and researchers. Any scientist dealing with systems that exhibit entropy will find the book an invaluable aid to their understanding.
Book Synopsis IEEE International Symposium on Information Theory by :
Download or read book IEEE International Symposium on Information Theory written by and published by . This book was released on 1985 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A User's Guide to Measure Theoretic Probability by : David Pollard
Download or read book A User's Guide to Measure Theoretic Probability written by David Pollard and published by Cambridge University Press. This book was released on 2002 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not just a presentation of mathematical theory, but is also a discussion of why that theory takes its current form. It will be a secure starting point for anyone who needs to invoke rigorous probabilistic arguments and understand what they mean.
Book Synopsis Nonparametric Econometrics by : Qi Li
Download or read book Nonparametric Econometrics written by Qi Li and published by Princeton University Press. This book was released on 2011-10-09 with total page 769 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive, up-to-date textbook on nonparametric methods for students and researchers Until now, students and researchers in nonparametric and semiparametric statistics and econometrics have had to turn to the latest journal articles to keep pace with these emerging methods of economic analysis. Nonparametric Econometrics fills a major gap by gathering together the most up-to-date theory and techniques and presenting them in a remarkably straightforward and accessible format. The empirical tests, data, and exercises included in this textbook help make it the ideal introduction for graduate students and an indispensable resource for researchers. Nonparametric and semiparametric methods have attracted a great deal of attention from statisticians in recent decades. While the majority of existing books on the subject operate from the presumption that the underlying data is strictly continuous in nature, more often than not social scientists deal with categorical data—nominal and ordinal—in applied settings. The conventional nonparametric approach to dealing with the presence of discrete variables is acknowledged to be unsatisfactory. This book is tailored to the needs of applied econometricians and social scientists. Qi Li and Jeffrey Racine emphasize nonparametric techniques suited to the rich array of data types—continuous, nominal, and ordinal—within one coherent framework. They also emphasize the properties of nonparametric estimators in the presence of potentially irrelevant variables. Nonparametric Econometrics covers all the material necessary to understand and apply nonparametric methods for real-world problems.
Book Synopsis Entropy, Large Deviations, and Statistical Mechanics by : Richard.S. Ellis
Download or read book Entropy, Large Deviations, and Statistical Mechanics written by Richard.S. Ellis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has two main topics: large deviations and equilibrium statistical mechanics. I hope to convince the reader that these topics have many points of contact and that in being treated together, they enrich each other. Entropy, in its various guises, is their common core. The large deviation theory which is developed in this book focuses upon convergence properties of certain stochastic systems. An elementary example is the weak law of large numbers. For each positive e, P{ISn/nl 2: e} con verges to zero as n --+ 00, where Sn is the nth partial sum of indepen dent identically distributed random variables with zero mean. Large deviation theory shows that if the random variables are exponentially bounded, then the probabilities converge to zero exponentially fast as n --+ 00. The exponen tial decay allows one to prove the stronger property of almost sure conver gence (Sn/n --+ 0 a.s.). This example will be generalized extensively in the book. We will treat a large class of stochastic systems which involve both indepen dent and dependent random variables and which have the following features: probabilities converge to zero exponentially fast as the size of the system increases; the exponential decay leads to strong convergence properties of the system. The most fascinating aspect of the theory is that the exponential decay rates are computable in terms of entropy functions. This identification between entropy and decay rates of large deviation probabilities enhances the theory significantly.
Book Synopsis High-Dimensional Probability by : Roman Vershynin
Download or read book High-Dimensional Probability written by Roman Vershynin and published by Cambridge University Press. This book was released on 2018-09-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Book Synopsis The Mathematics of Information Coding, Extraction and Distribution by : George Cybenko
Download or read book The Mathematics of Information Coding, Extraction and Distribution written by George Cybenko and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: High performance computing consumes and generates vast amounts of data, and the storage, retrieval, and transmission of this data are major obstacles to effective use of computing power. Challenges inherent in all of these operations are security, speed, reliability, authentication and reproducibility. This workshop focused on a wide variety of technical results aimed at meeting these challenges. Topics ranging from the mathematics of coding theory to the practicalities of copyright preservation for Internet resources drew spirited discussion and interaction among experts in diverse but related fields. We hope this volume contributes to continuing this dialogue.
Book Synopsis Introduction to Empirical Processes and Semiparametric Inference by : Michael R. Kosorok
Download or read book Introduction to Empirical Processes and Semiparametric Inference written by Michael R. Kosorok and published by Springer Science & Business Media. This book was released on 2007-12-29 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kosorok’s brilliant text provides a self-contained introduction to empirical processes and semiparametric inference. These powerful research techniques are surprisingly useful for developing methods of statistical inference for complex models and in understanding the properties of such methods. This is an authoritative text that covers all the bases, and also a friendly and gradual introduction to the area. The book can be used as research reference and textbook.
