The Maximum Entropy Method

Author: Nailong Wu
Publisher: Springer Science & Business Media
ISBN: 9783642606298
Release Date: 2012-12-06
Genre: Science

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.

Energy Minimization Methods in Computer Vision and Pattern Recognition

Author: Edwin R. Hancock
Publisher: Springer
ISBN: 9783540484325
Release Date: 2003-07-31
Genre: Computers

This book constitutes the refereed proceedings of the Second International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition, EMMCVPR'99, held in York, UK in July 1999. The book presents 11 revised full papers together with 11 papers presented at the meeting as posters. Those papers were selected from a total of 33 submissions. The book is divided in sections on shape, minimum description length, Markov random fields, contours, search and consistent labeling, tracking and video, and biomedical applications.

Muon Spin Rotation Relaxation and Resonance

Author: Alain Yaouanc
Publisher: Oxford University Press
ISBN: 9780199596478
Release Date: 2011
Genre: Science

Intended for graduate students and researchers who plan to use the muon spin rotation and relaxation techniques. A comprehensive discussion of the information extracted from measurements on magnetic and superconductor materials. The muonium centres as well as the muon and muonium diffusion in materials are discussed.

Maximum Entropy and Bayesian Methods in Science and Engineering

Author: G. Erickson
Publisher: Springer Science & Business Media
ISBN: 9027727945
Release Date: 1988-08-31
Genre: Mathematics

This volume has its origin in the Fifth, Sixth and Seventh Workshops on "Maximum-Entropy and Bayesian Methods in Applied Statistics", held at 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 most of the papers in this volume 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 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. These workshops and their proceedings could not have been brought to their final form without the support or help of a number of people.

Entropy Measures Maximum Entropy Principle and Emerging Applications

Author: Karmeshu
Publisher: Springer
ISBN: 9783540362128
Release Date: 2012-10-01
Genre: Mathematics

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.

From Statistical Physics to Statistical Inference and Back

Author: P. Grassberger
Publisher: Springer Science & Business Media
ISBN: 9789401110686
Release Date: 2012-12-06
Genre: Science

Physicists, when modelling physical systems with a large number of degrees of freedom, and statisticians, when performing data analysis, have developed their own concepts and methods for making the `best' inference. But are these methods equivalent, or not? What is the state of the art in making inferences? The physicists want answers. More: neural computation demands a clearer understanding of how neural systems make inferences; the theory of chaotic nonlinear systems as applied to time series analysis could profit from the experience already booked by the statisticians; and finally, there is a long-standing conjecture that some of the puzzles of quantum mechanics are due to our incomplete understanding of how we make inferences. Matter enough to stimulate the writing of such a book as the present one. But other considerations also arise, such as the maximum entropy method and Bayesian inference, information theory and the minimum description length. Finally, it is pointed out that an understanding of human inference may require input from psychologists. This lively debate, which is of acute current interest, is well summarized in the present work.

Bayesian Inference and Maximum Entropy Methods in Science and Engineering

Author: Ali Mohammad-Djafari
Publisher: American Inst. of Physics
ISBN: 0735403716
Release Date: 2006-12-13
Genre: Mathematics

The MaxEnt workshops are devoted to Bayesian inference and maximum entropy methods in science and engineering. In addition, this workshop included all aspects of probabilistic inference, such as foundations, techniques, algorithms, and applications. All papers have been peer-reviewed.

Entropy Based Parameter Estimation in Hydrology

Author: V.P. Singh
Publisher: Springer Science & Business Media
ISBN: 9789401714310
Release Date: 2013-04-17
Genre: Science

Since the pioneering work of Shannon in the late 1940's on the development of the theory of entropy and the landmark contributions of Jaynes a decade later leading to the development of the principle of maximum entropy (POME), the concept of entropy has been increasingly applied in a wide spectrum of areas, including chemistry, electronics and communications engineering, data acquisition and storage and retreival, data monitoring network design, ecology, economics, environmental engineering, earth sciences, fluid mechanics, genetics, geology, geomorphology, geophysics, geotechnical engineering, hydraulics, hydrology, image processing, management sciences, operations research, pattern recognition and identification, photogrammetry, psychology, physics and quantum mechanics, reliability analysis, reservoir engineering, statistical mechanics, thermodynamics, topology, transportation engineering, turbulence modeling, and so on. New areas finding application of entropy have since continued to unfold. The entropy concept is indeed versatile and its applicability widespread. In the area of hydrology and water resources, a range of applications of entropy have been reported during the past three decades or so. This book focuses on parameter estimation using entropy for a number of distributions frequently used in hydrology. In the entropy-based parameter estimation the distribution parameters are expressed in terms of the given information, called constraints. Thus, the method lends itself to a physical interpretation of the parameters. Because the information to be specified usually constitutes sufficient statistics for the distribution under consideration, the entropy method provides a quantitative way to express the information contained in the distribution.

Maximum Entropy and Bayesian Methods

Author: P.F. Fougère
Publisher: Springer Science & Business Media
ISBN: 9789400906839
Release Date: 2012-12-06
Genre: Mathematics

This volume represents the proceedings of the Ninth Annual MaxEnt Workshop, held at Dartmouth College in Hanover, New Hampshire, on August 14-18, 1989. These annual meetings are devoted to the theory and practice of Bayesian Probability and the Maximum Entropy Formalism. The fields of application exemplified at MaxEnt '89 are as diverse as the foundations of probability theory and atmospheric carbon variations, the 1987 Supernova and fundamental quantum mechanics. Subjects include sea floor drug absorption in man, pressures, neutron scattering, plasma equilibrium, nuclear magnetic resonance, radar and astrophysical image reconstruction, mass spectrometry, generalized parameter estimation, delay estimation, pattern recognition, heave responses in underwater sound and many others. The first ten papers are on probability theory, and are grouped together beginning with the most abstract followed by those on applications. The tenth paper involves both Bayesian and MaxEnt methods and serves as a bridge to the remaining papers which are devoted to Maximum Entropy theory and practice. Once again, an attempt has been made to start with the more theoretical papers and to follow them with more and more practical applications. Papers number 29, 30 and 31, by Kesaven, Seth and Kapur, represent a somewhat different, perhaps even "unorthodox" viewpoint, and are included here even though the editor and, indeed many in the audience at Dartmouth, disagreed with their content. I feel that scientific disagreements are essential in any developing field, and often lead to a deeper understanding.