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The Method Of Maximum Entropy


The Method Of Maximum Entropy
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The Maximum Entropy Method


The Maximum Entropy Method
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Author : Nailong Wu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

The Maximum Entropy Method written by Nailong Wu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.


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 Method Of Maximum Entropy


The Method Of Maximum Entropy
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Author : Henryk Gzyl
language : en
Publisher: World Scientific
Release Date : 1995-03-16

The Method Of Maximum Entropy written by Henryk Gzyl and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-03-16 with Mathematics categories.


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.



Maximum Entropy And Bayesian Methods In Science And Engineering


Maximum Entropy And Bayesian Methods In Science And Engineering
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Author : G. Erickson
language : en
Publisher: Springer Science & Business Media
Release Date : 1988-08-31

Maximum Entropy And Bayesian Methods In Science And Engineering written by G. Erickson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-08-31 with Mathematics categories.


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.



Maximum Entropy And Ecology


Maximum Entropy And Ecology
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Author : John Harte
language : en
Publisher: OUP Oxford
Release Date : 2011-06-23

Maximum Entropy And Ecology written by John Harte and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-23 with Science categories.


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.



Bayesian Inference And Maximum Entropy Methods In Science And Engineering


Bayesian Inference And Maximum Entropy Methods In Science And Engineering
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Author : Adriano Polpo
language : en
Publisher: Springer
Release Date : 2018-07-12

Bayesian Inference And Maximum Entropy Methods In Science And Engineering written by Adriano Polpo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-12 with Mathematics categories.


These proceedings from the 37th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2017), held in São Carlos, Brazil, aim to expand the available research on Bayesian methods and promote their application in the scientific community. They gather research from scholars in many different fields who use inductive statistics methods and focus on the foundations of the Bayesian paradigm, their comparison to objectivistic or frequentist statistics counterparts, and their appropriate applications. Interest in the foundations of inductive statistics has been growing with the increasing availability of Bayesian methodological alternatives, and scientists now face much more difficult choices in finding the optimal methods to apply to their problems. By carefully examining and discussing the relevant foundations, the scientific community can avoid applying Bayesian methods on a merely ad hoc basis. For over 35 years, the MaxEnt workshops have explored the use of Bayesian and Maximum Entropy methods in scientific and engineering application contexts. The workshops welcome contributions on all aspects of probabilistic inference, including novel techniques and applications, and work that sheds new light on the foundations of inference. Areas of application in these workshops include astronomy and astrophysics, chemistry, communications theory, cosmology, climate studies, earth science, fluid mechanics, genetics, geophysics, machine learning, materials science, medical imaging, nanoscience, source separation, thermodynamics (equilibrium and non-equilibrium), particle physics, plasma physics, quantum mechanics, robotics, and the social sciences. Bayesian computational techniques such as Markov chain Monte Carlo sampling are also regular topics, as are approximate inferential methods. Foundational issues involving probability theory and information theory, as well as novel applications of inference to illuminate the foundations of physical theories, are also of keen interest.



Maximum Entropy Econometrics


Maximum Entropy Econometrics
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Author : Amos Golan
language : en
Publisher: John Wiley & Sons
Release Date : 1996-05

Maximum Entropy Econometrics written by Amos Golan and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-05 with Business & Economics categories.


This monograph examines the problem of recovering and processing information when the underlying data are limited or partial, and the corresponding models that form the basis for estimation and inference are ill-posed or undermined



Linear Inverse Problems


Linear Inverse Problems
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Author : Henryk Gzyl
language : en
Publisher: World Scientific
Release Date : 2011

Linear Inverse Problems written by Henryk Gzyl and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.


The book describes a useful tool for solving linear inverse problems subject to convex constraints. The method of maximum entropy in the mean automatically takes care of the constraints. It consists of a technique for transforming a large dimensional inverse problem into a small dimensional non-linear variational problem. A variety of mathematical aspects of the maximum entropy method are explored as well.



Maximum Entropy And Bayesian Methods In Applied Statistics


Maximum Entropy And Bayesian Methods In Applied Statistics
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Author : James H. Justice
language : en
Publisher: Cambridge University Press
Release Date : 2009-01-11

Maximum Entropy And Bayesian Methods In Applied Statistics written by James H. Justice and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-11 with Mathematics categories.


This collection of papers by leading researchers in their respective fields contains contributions showing the use of the maximum entropy method in many of the fields in which it finds application. In the physical, mathematical and biological sciences it is often necessary to make inferences based on insufficient data. The problem of choosing one among the many possible conclusions or models which are compatible with the data may be resolved in a variety of ways. A particularly appealing method is to choose the solution which maximizes entropy in the sense that the conclusion or model honours the observed data but implies no further assumptions not warranted by the data. The maximum entropy principle has been growing in importance and acceptance in many fields, perhaps most notably statistical physics, astronomy, geophysics, signal processing, image analysis and physical chemistry. The papers included in this volume touch on most of the current areas of research activity and application, and will be of interest to research workers in all fields in which the maximum entropy method may be applied.



Maximum Entropy And Bayesian Methods


Maximum Entropy And Bayesian Methods
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Author : John Skilling
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29

Maximum Entropy And Bayesian Methods written by John Skilling and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.


Cambridge, England, 1988