Axiomatic Derivation Of The Principle Of Maximum Entropy And The Principle Of Minimum Cross Entropy

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Axiomatic Derivation of the Principle of Maximum Entropy and the Principle of Minimum Cross-Entropy

Author : John E. Shore
Publisher :
ISBN 13 :
Total Pages : 63 pages
Book Rating : 4.:/5 (227 download)

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Book Synopsis Axiomatic Derivation of the Principle of Maximum Entropy and the Principle of Minimum Cross-Entropy by : John E. Shore

Download or read book Axiomatic Derivation of the Principle of Maximum Entropy and the Principle of Minimum Cross-Entropy written by John E. Shore and published by . This book was released on 1978 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: We prove that, in a well-defined sense, Jaynes's principle of maximum entropy and Kullback's principle of minimum cross-entropy (minimum directed divergence) provide uniquely correct, general methods of inductive inference when new information is given in the form of expected values. Previous justifications rely heavily on intuitive arguments and on the properties of entropy and cross-entropy as information measures. Our approach assumes that reasonable methods of inductive inference should lead to consistent results whenever there are different ways of taking the same information into account --- for example, in different coordinate systems. We formalize this requirement as four consistency axioms stated in terms of an abstract information operator; the axioms make no reference to information measures. We establish this result both directly and as a special case (uniform priors) of an analogous, more general result for the principle of minimum cross-entropy. We obtain results both for continuous probability densities and for discrete distributions.

Entropy Optimization Principles with Applications

Author : Jagat Narain Kapur
Publisher :
ISBN 13 :
Total Pages : 440 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Entropy Optimization Principles with Applications by : Jagat Narain Kapur

Download or read book Entropy Optimization Principles with Applications written by Jagat Narain Kapur and published by . This book was released on 1992 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This senior-level textbook on entropy provides a conceptual framework for the study of probabilistic systems with its elucidation of three key concepts - Shannon's information theory, Jaynes' maximum entropy principle and Kullback's minimum cross-entropy principle.

Maximum Entropy Principle and the Minimum Cross Entropy Principle

Author : Everton Rowe
Publisher :
ISBN 13 :
Total Pages : 262 pages
Book Rating : 4.:/5 (71 download)

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Book Synopsis Maximum Entropy Principle and the Minimum Cross Entropy Principle by : Everton Rowe

Download or read book Maximum Entropy Principle and the Minimum Cross Entropy Principle written by Everton Rowe and published by . This book was released on 1985 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

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

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.

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 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.

Encyclopedia of Optimization

Author : Christodoulos A. Floudas
Publisher : Springer Science & Business Media
ISBN 13 : 0387747583
Total Pages : 4646 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Encyclopedia of Optimization by : Christodoulos A. Floudas

Download or read book Encyclopedia of Optimization written by Christodoulos A. Floudas and published by Springer Science & Business Media. This book was released on 2008-09-04 with total page 4646 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Data Analysis

Author : D. S. Sivia
Publisher : Oxford University Press
ISBN 13 : 9780198518891
Total Pages : 212 pages
Book Rating : 4.5/5 (188 download)

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Book Synopsis Data Analysis by : D. S. Sivia

Download or read book Data Analysis written by D. S. Sivia and published by Oxford University Press. This book was released on 1996 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistics lectures have often been viewed with trepidation by engineering and science students taking an ancillary course in this subject. Whereas there are many texts showing "how" statistical methods are applied, few provide a clear explanation for non-statisticians of how the principlesof data analysis can be based on probability theory. Data Analysis: A Bayesian Tutorial provides such a text, putting emphasis as much on understanding "why" and "when" certain statistical procedures should be used as "how". This difference in approach makes the text ideal as a tutorial guide forsenior undergraduates and research students, in science and engineering. After explaining the basic principles of Bayesian probability theory, their use is illustrated with a variety of examples ranging from elementary parameter estimation to image processing. With its central emphasis on a fewfundamental rules, this book takes the mystery out of statistics by providing a clear rationale for some of the most widely-used procedures.

Conditionals in Nonmonotonic Reasoning and Belief Revision

Author : Gabriele Kern-Isberner
Publisher : Springer
ISBN 13 : 3540446001
Total Pages : 194 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Conditionals in Nonmonotonic Reasoning and Belief Revision by : Gabriele Kern-Isberner

Download or read book Conditionals in Nonmonotonic Reasoning and Belief Revision written by Gabriele Kern-Isberner and published by Springer. This book was released on 2003-06-29 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conditionals are omnipresent, in everyday life as well as in scientific environments; they represent generic knowledge acquired inductively or learned from books. They tie a flexible and highly interrelated network of connections along which reasoning is possible and which can be applied to different situations. Therefore, conditionals are important, but also quite problematic objects in knowledge representation. This book presents a new approach to conditionals which captures their dynamic, non-proportional nature particularly well by considering conditionals as agents shifting possible worlds in order to establish relationships and beliefs. This understanding of conditionals yields a rich theory which makes complex interactions between conditionals transparent and operational. Moreover,it provides a unifying and enhanced framework for knowledge representation, nonmonotonic reasoning, belief revision,and even for knowledge discovery.

Description Logic, Theory Combination, and All That

Author : Carsten Lutz
Publisher : Springer
ISBN 13 : 3030221024
Total Pages : 662 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Description Logic, Theory Combination, and All That by : Carsten Lutz

Download or read book Description Logic, Theory Combination, and All That written by Carsten Lutz and published by Springer. This book was released on 2019-06-25 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Festschrift has been put together on the occasion of Franz Baader's 60th birthday to celebrate his fundamental and highly influential scientific contributions. The 30 papers in this volume cover several scientific areas that Franz Baader has been working on during the last three decades, including description logics, term rewriting, and the combination of decision procedures. We hope that readers will enjoy the articles gathered in Franz's honour and appreciate the breadth and depth of his favourite areas of computer science.

Econometric Foundations Pack with CD-ROM

Author : Ron Mittelhammer (Prof.)
Publisher : Cambridge University Press
ISBN 13 : 9780521623940
Total Pages : 794 pages
Book Rating : 4.6/5 (239 download)

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Book Synopsis Econometric Foundations Pack with CD-ROM by : Ron Mittelhammer (Prof.)

Download or read book Econometric Foundations Pack with CD-ROM written by Ron Mittelhammer (Prof.) and published by Cambridge University Press. This book was released on 2000-07-28 with total page 794 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text and accompanying CD-ROM develop step by step a modern approach to econometric problems. They are aimed at talented upper-level undergraduates, graduate students, and professionals wishing to acquaint themselves with the pinciples and procedures for information processing and recovery from samples of economic data. The text fully provides an operational understanding of a rich set of estimation and inference tools, including tradional likelihood based and non-traditional non-likelihood based procedures, that can be used in conjuction with the computer to address economic problems.

Symbolic and Quantitative Approaches to Reasoning with Uncertainty

Author : Thomas D. Nielsen
Publisher : Springer
ISBN 13 : 3540450629
Total Pages : 619 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Symbolic and Quantitative Approaches to Reasoning with Uncertainty by : Thomas D. Nielsen

Download or read book Symbolic and Quantitative Approaches to Reasoning with Uncertainty written by Thomas D. Nielsen and published by Springer. This book was released on 2004-04-07 with total page 619 pages. Available in PDF, EPUB and Kindle. Book excerpt: The refereed proceedings of the 7th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2003, held in Aalborg, Denmark in July 2003. The 47 revised full papers presented together with 2 invited survey articles were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on foundations of uncertainty concepts, Bayesian networks, algorithms for uncertainty inference, learning, decision graphs, belief functions, fuzzy sets, possibility theory, default reasoning, belief revision and inconsistency handling, logics, and tools.

Multirate Statistical Signal Processing

Author : Omid S. Jahromi
Publisher : Springer Science & Business Media
ISBN 13 : 1402053177
Total Pages : 178 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Multirate Statistical Signal Processing by : Omid S. Jahromi

Download or read book Multirate Statistical Signal Processing written by Omid S. Jahromi and published by Springer Science & Business Media. This book was released on 2007-05-15 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multirate Statistical Signal Processing introduces a statistical theory for extracting information from related signals with different sampling rates. This new theory generalizes the conventional deterministic theory of multirate systems beyond many of its constraints. Further, it allows for the formulation and solution of new problems: spectrum estimation, time-delay estimation and sensor fusion in the realm of multirate signal processing. This self-contained book presents background material, potential applications and leading-edge research.

Advances in Chemical Physics, Volume 162

Author : Stuart A. Rice
Publisher : John Wiley & Sons
ISBN 13 : 1119324572
Total Pages : 371 pages
Book Rating : 4.1/5 (193 download)

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Book Synopsis Advances in Chemical Physics, Volume 162 by : Stuart A. Rice

Download or read book Advances in Chemical Physics, Volume 162 written by Stuart A. Rice and published by John Wiley & Sons. This book was released on 2017-10-09 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Advances in Chemical Physics series provides the chemical physics field with a forum for critical, authoritative evaluations of advances in every area of the discipline. • This is the only series of volumes available that presents the cutting edge of research in chemical physics. • Includes contributions from experts in this field of research. • Contains a representative cross-section of research that questions established thinking on chemical solutions • Structured with an editorial framework that makes the book an excellent supplement to an advanced graduate class in physical chemistry or chemical physics

Maximum-Entropy and Bayesian Spectral Analysis and Estimation Problems

Author : C.R. Smith
Publisher : Springer Science & Business Media
ISBN 13 : 9400939612
Total Pages : 322 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Maximum-Entropy and Bayesian Spectral Analysis and Estimation Problems by : C.R. Smith

Download or read book Maximum-Entropy and Bayesian Spectral Analysis and Estimation Problems written by C.R. Smith and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume has its origin in the third ·Workshop on Maximum-Entropy and Bayesian Methods in Applied Statistics,· held at the University of Wyoming, August 1 to 4, 1983. It was anticipated that the proceedings of this workshop could not be prepared in a timely fashion, so most of the papers were not collected until a year or so ago. Because most of the papers are in the nature of advancing theory or solving specific problems, as opposed to status reports, it is believed that the contents of this volume will be of lasting interest to the Bayesian community. The workshop was organized to bring together researchers from differ ent fields to examine critically maximum-entropy and Bayesian methods in science, engineering, medicine, economics, and 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 Bayes ian method.