The Maximum Entropy Distribution

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Maximum-entropy Models in Science and Engineering

Author : Jagat Narain Kapur
Publisher : John Wiley & Sons
ISBN 13 : 9788122402162
Total Pages : 660 pages
Book Rating : 4.4/5 (21 download)

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Book Synopsis Maximum-entropy Models in Science and Engineering by : Jagat Narain Kapur

Download or read book Maximum-entropy Models in Science and Engineering written by Jagat Narain Kapur and published by John Wiley & Sons. This book was released on 1989 with total page 660 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Is The First Comprehensive Book About Maximum Entropy Principle And Its Applications To A Diversity Of Fields Like Statistical Mechanics, Thermo-Dynamics, Business, Economics, Insurance, Finance, Contingency Tables, Characterisation Of Probability Distributions (Univariate As Well As Multivariate, Discrete As Well As Continuous), Statistical Inference, Non-Linear Spectral Analysis Of Time Series, Pattern Recognition, Marketing And Elections, Operations Research And Reliability Theory, Image Processing, Computerised Tomography, Biology And Medicine. There Are Over 600 Specially Constructed Exercises And Extensive Historical And Bibliographical Notes At The End Of Each Chapter.The Book Should Be Of Interest To All Applied Mathematicians, Physicists, Statisticians, Economists, Engineers Of All Types, Business Scientists, Life Scientists, Medical Scientists, Radiologists And Operations Researchers Who Are Interested In Applying The Powerful Methodology Based On Maximum Entropy Principle In Their Respective Fields.

Maximum Entropy and Ecology

Author : John Harte
Publisher : OUP Oxford
ISBN 13 : 0191621161
Total Pages : 280 pages
Book Rating : 4.1/5 (916 download)

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Book Synopsis Maximum Entropy and Ecology by : John Harte

Download or read book Maximum Entropy and Ecology written by John Harte and published by OUP Oxford. This book was released on 2011-06-23 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This pioneering graduate textbook provides readers with the concepts and practical tools required to understand the maximum entropy principle, and apply it to an understanding of ecological patterns. Rather than building and combining mechanistic models of ecosystems, the approach is grounded in information theory and the logic of inference. Paralleling the derivation of thermodynamics from the maximum entropy principle, the state variable theory of ecology developed in this book predicts realistic forms for all metrics of ecology that describe patterns in the distribution, abundance, and energetics of species over multiple spatial scales, a wide range of habitats, and diverse taxonomic groups. The first part of the book is foundational, discussing the nature of theory, the relationship of ecology to other sciences, and the concept of the logic of inference. Subsequent sections present the fundamentals of macroecology and of maximum information entropy, starting from first principles. The core of the book integrates these fundamental principles, leading to the derivation and testing of the predictions of the maximum entropy theory of ecology (METE). A final section broadens the book's perspective by showing how METE can help clarify several major issues in conservation biology, placing it in context with other theories and highlighting avenues for future research.

Maximum-Entropy and Bayesian Methods in Science and Engineering

Author : G. Erickson
Publisher : Springer Science & Business Media
ISBN 13 : 9789027727930
Total Pages : 338 pages
Book Rating : 4.7/5 (279 download)

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Book Synopsis Maximum-Entropy and Bayesian Methods in Science and Engineering by : G. Erickson

Download or read book Maximum-Entropy and Bayesian Methods in Science and Engineering written by G. Erickson and published by Springer Science & Business Media. This book was released on 1988-08-31 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume has its origin in the Fifth, Sixth and Seventh Workshops on and Bayesian Methods in Applied Statistics", held at "Maximum-Entropy the University of Wyoming, August 5-8, 1985, and at Seattle University, August 5-8, 1986, and August 4-7, 1987. It was anticipated that the proceedings of these workshops would be combined, so most of the papers were not collected until after the seventh workshop. Because all of the papers in this volume are on foundations, it is believed that the con tents of this volume will be of lasting interest to the Bayesian community. The workshop was organized to bring together researchers from different fields to critically examine maximum-entropy and Bayesian methods in science and engineering as well as other disciplines. Some of the papers were chosen specifically to kindle interest in new areas that may offer new tools or insight to the reader or to stimulate work on pressing problems that appear to be ideally suited to the maximum-entropy or Bayesian method. A few papers presented at the workshops are not included in these proceedings, but a number of additional papers not presented at the workshop are included. In particular, we are delighted to make available Professor E. T. Jaynes' unpublished Stanford University Microwave Laboratory Report No. 421 "How Does the Brain Do Plausible Reasoning?" (dated August 1957). This is a beautiful, detailed tutorial on the Cox-Polya-Jaynes approach to Bayesian probability theory and the maximum-entropy principle.

The Maximum Entropy Distribution

Author : Henri Theil
Publisher :
ISBN 13 :
Total Pages : 158 pages
Book Rating : 4.:/5 (287 download)

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Book Synopsis The Maximum Entropy Distribution by : Henri Theil

Download or read book The Maximum Entropy Distribution written by Henri Theil and published by . This book was released on 1981 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Method Of Maximum Entropy

Author : Henryk Gzyl
Publisher : World Scientific
ISBN 13 : 9814501921
Total Pages : 161 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis The Method Of Maximum Entropy by : Henryk Gzyl

Download or read book The Method Of Maximum Entropy written by Henryk Gzyl and published by World Scientific. This book was released on 1995-03-16 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is an outgrowth of a set of lecture notes on the maximum entropy method delivered at the 1st Venezuelan School of Mathematics. This yearly event aims at acquainting graduate students and university teachers with the trends, techniques and open problems of current interest. In this book the author reviews several versions of the maximum entropy method and makes its underlying philosophy clear.

The Maximum Entropy Distribution

Author : Henri Theil
Publisher :
ISBN 13 :
Total Pages : 65 pages
Book Rating : 4.:/5 (11 download)

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Book Synopsis The Maximum Entropy Distribution by : Henri Theil

Download or read book The Maximum Entropy Distribution written by Henri Theil and published by . This book was released on 1980 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Maximum Entropy and Bayesian Methods

Author : John Skilling
Publisher : Springer Science & Business Media
ISBN 13 : 9401578605
Total Pages : 521 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Maximum Entropy and Bayesian Methods by : John Skilling

Download or read book Maximum Entropy and Bayesian Methods written by John Skilling and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cambridge, England, 1988

Maximum Entropy and Bayesian Methods

Author : C.R. Smith
Publisher : Springer
ISBN 13 : 9789048142200
Total Pages : 0 pages
Book Rating : 4.1/5 (422 download)

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Book Synopsis Maximum Entropy and Bayesian Methods by : C.R. Smith

Download or read book Maximum Entropy and Bayesian Methods written by C.R. Smith and published by Springer. This book was released on 2010-12-05 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian probability theory and maximum entropy methods are at the core of a new view of scientific inference. These `new' ideas, along with the revolution in computational methods afforded by modern computers, allow astronomers, electrical engineers, image processors of any type, NMR chemists and physicists, and anyone at all who has to deal with incomplete and noisy data, to take advantage of methods that, in the past, have been applied only in some areas of theoretical physics. This volume records the Proceedings of Eleventh Annual `Maximum Entropy' Workshop, held at Seattle University in June, 1991. These workshops have been the focus of a group of researchers from many different fields, and this diversity is evident in this volume. There are tutorial papers, theoretical papers, and applications in a very wide variety of fields. Almost any instance of dealing with incomplete and noisy data can be usefully treated by these methods, and many areas of theoretical research are being enhanced by the thoughtful application of Bayes' theorem. The contributions contained in this volume present a state-of-the-art review that will be influential and useful for many years to come.

Maximum Entropy Probability Distribution

Author : Jenny Farmer
Publisher :
ISBN 13 :
Total Pages : 140 pages
Book Rating : 4.:/5 (885 download)

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Book Synopsis Maximum Entropy Probability Distribution by : Jenny Farmer

Download or read book Maximum Entropy Probability Distribution written by Jenny Farmer and published by . This book was released on 2014 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given a set of randomly sampled experimental data, a numeric algorithm has been developed to determine a probability distribution function that represents the data. The algorithm is based on the maximum entropy method in information theory, which states that the solution that maximizes entropy while satisfying known constraints is presumed to be the correct solution. The probability distribution function is expressed as an exponential of a series expansion over Chebyshev polynomials where the expansion coefficients are formally Lagrange multipliers and must be determined. The method for finding these Lagrange multipliers is through an iterative trial-and-error approach. After each guess for the coefficients, the trial solution is evaluated according to how well it represents the data. This assessment is performed by using the cumulative distribution function to transform the data to uniformly distributed random data, and then comparing the transformed data to known results for a uniform distribution using binning and ordered statistics. The algorithm is presented in the form of a highly adaptive and flexible tool that does not assume prior knowledge about the data, but provides many documented settings to allow for maximum efficiency in the event the user has more information about the data or has specific requirements. To demonstrate the power and flexibility of this approach, it has been tested and compared against known distributions, many of which have specific properties known to cause standard methods to fail. Each of these examples demonstrates a convergence to the true function as the sample size increases.

Entropy Measures, Maximum Entropy Principle and Emerging Applications

Author : Karmeshu
Publisher : Springer
ISBN 13 : 3540362126
Total Pages : 300 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Entropy Measures, Maximum Entropy Principle and Emerging Applications by : Karmeshu

Download or read book Entropy Measures, Maximum Entropy Principle and Emerging Applications written by Karmeshu and published by Springer. This book was released on 2012-10-01 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last two decades have witnessed an enormous growth with regard to ap plications of information theoretic framework in areas of physical, biological, engineering and even social sciences. In particular, growth has been spectac ular in the field of information technology,soft computing,nonlinear systems and molecular biology. Claude Shannon in 1948 laid the foundation of the field of information theory in the context of communication theory. It is in deed remarkable that his framework is as relevant today as was when he 1 proposed it. Shannon died on Feb 24, 2001. Arun Netravali observes "As if assuming that inexpensive, high-speed processing would come to pass, Shan non figured out the upper limits on communication rates. First in telephone channels, then in optical communications, and now in wireless, Shannon has had the utmost value in defining the engineering limits we face". Shannon introduced the concept of entropy. The notable feature of the entropy frame work is that it enables quantification of uncertainty present in a system. In many realistic situations one is confronted only with partial or incomplete information in the form of moment, or bounds on these values etc. ; and it is then required to construct a probabilistic model from this partial information. In such situations, the principle of maximum entropy provides a rational ba sis for constructing a probabilistic model. It is thus necessary and important to keep track of advances in the applications of maximum entropy principle to ever expanding areas of knowledge.

An Introduction to Information Theory

Author : Fazlollah M. Reza
Publisher :
ISBN 13 :
Total Pages : 532 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis An Introduction to Information Theory by : Fazlollah M. Reza

Download or read book An Introduction to Information Theory written by Fazlollah M. Reza and published by . This book was released on 1961 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Extension of Positive-Definite Distributions and Maximum Entropy

Author : Jean-Pierre Gabardo
Publisher : American Mathematical Soc.
ISBN 13 : 0821825518
Total Pages : 111 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Extension of Positive-Definite Distributions and Maximum Entropy by : Jean-Pierre Gabardo

Download or read book Extension of Positive-Definite Distributions and Maximum Entropy written by Jean-Pierre Gabardo and published by American Mathematical Soc.. This book was released on 1993 with total page 111 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work, the maximum entropy method is used to solve the extension problem associated with a positive-definite function, or distribution, defined on an interval of the real line. Garbardo computes explicitly the entropy maximizers corresponding to various logarithmic integrals depending on a complex parameter and investigates the relation to the problem of uniqueness of the extension. These results are based on a generalization, in both the discrete and continuous cases, of Burg's maximum entropy theorem.

The Maximum Entropy Method

Author : Nailong Wu
Publisher : Springer Science & Business Media
ISBN 13 : 3642606296
Total Pages : 336 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis The Maximum Entropy Method by : Nailong Wu

Download or read book The Maximum Entropy Method written by Nailong Wu and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Forty years ago, in 1957, the Principle of Maximum Entropy was first intro duced by Jaynes into the field of statistical mechanics. Since that seminal publication, this principle has been adopted in many areas of science and technology beyond its initial application. It is now found in spectral analysis, image restoration and a number of branches ofmathematics and physics, and has become better known as the Maximum Entropy Method (MEM). Today MEM is a powerful means to deal with ill-posed problems, and much research work is devoted to it. My own research in the area ofMEM started in 1980, when I was a grad uate student in the Department of Electrical Engineering at the University of Sydney, Australia. This research work was the basis of my Ph.D. the sis, The Maximum Entropy Method and Its Application in Radio Astronomy, completed in 1985. As well as continuing my research in MEM after graduation, I taught a course of the same name at the Graduate School, Chinese Academy of Sciences, Beijingfrom 1987to 1990. Delivering the course was theimpetus for developing a structured approach to the understanding of MEM and writing hundreds of pages of lecture notes.

The Maximum Entropy Distribution and Its Covariance Matrix

Author : Denzil Gwydir Fiebig
Publisher :
ISBN 13 :
Total Pages : 344 pages
Book Rating : 4.:/5 (911 download)

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Book Synopsis The Maximum Entropy Distribution and Its Covariance Matrix by : Denzil Gwydir Fiebig

Download or read book The Maximum Entropy Distribution and Its Covariance Matrix written by Denzil Gwydir Fiebig and published by . This book was released on 1982 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Loss Data Analysis

Author : Henryk Gzyl
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110516136
Total Pages : 235 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Loss Data Analysis by : Henryk Gzyl

Download or read book Loss Data Analysis written by Henryk Gzyl and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-02-05 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with two complementary topics. On one hand the book deals with the problem of determining the the probability distribution of a positive compound random variable, a problem which appears in the banking and insurance industries, in many areas of operational research and in reliability problems in the engineering sciences. On the other hand, the methodology proposed to solve such problems, which is based on an application of the maximum entropy method to invert the Laplace transform of the distributions, can be applied to many other problems. The book contains applications to a large variety of problems, including the problem of dependence of the sample data used to estimate empirically the Laplace transform of the random variable. Contents Introduction Frequency models Individual severity models Some detailed examples Some traditional approaches to the aggregation problem Laplace transforms and fractional moment problems The standard maximum entropy method Extensions of the method of maximum entropy Superresolution in maxentropic Laplace transform inversion Sample data dependence Disentangling frequencies and decompounding losses Computations using the maxentropic density Review of statistical procedures

Topics in Circular Statistics

Author : S. Rao Jammalamadaka
Publisher : World Scientific
ISBN 13 : 9810237782
Total Pages : 336 pages
Book Rating : 4.8/5 (12 download)

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Book Synopsis Topics in Circular Statistics by : S. Rao Jammalamadaka

Download or read book Topics in Circular Statistics written by S. Rao Jammalamadaka and published by World Scientific. This book was released on 2001 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph on circular data analysis covers some recent advances in the field, besides providing a brief introduction to, and a review of, existing methods and models. The primary focus is on recent research into topics such as change-point problems, predictive distributions, circular correlation and regression, etc. An important feature of this work is the S-plus subroutines provided for analyzing actual data sets. Coupled with the discussion of new theoretical research, the book should benefit both the researcher and the practitioner.

Maximum Entropy in Action

Author : Brian Buck
Publisher : Oxford : Clarendon Press ; New York : Oxford University Press
ISBN 13 :
Total Pages : 260 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Maximum Entropy in Action by : Brian Buck

Download or read book Maximum Entropy in Action written by Brian Buck and published by Oxford : Clarendon Press ; New York : Oxford University Press. This book was released on 1991 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of introductory, interdisciplinary articles and lectures covering the fundamentals of the maximum entropy approach, a powerful new technique that provides a much needed extension of the established principles of rational inference in the sciences. Maximum entropy allows the interpretation of incomplete and "noisy" data, providing a description of the underlying physical systems. It has found application in both practical and theoretical studies ranging from image enhancement to nuclear physics, and from statistical mechanics to economics. The work explores these applications with specific problems of data analysis taken from the physical sciences. It will interest all physical scientists who deal with data and its interpretation, including statisticians and statistical physicists.