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Author: Nailong Wu Publisher: Springer Science & Business Media ISBN: 3642606296 Category : Science Languages : en Pages : 336
Book Description
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.
Author: Nailong Wu Publisher: Springer Science & Business Media ISBN: 3642606296 Category : Science Languages : en Pages : 336
Book Description
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.
Author: Henryk Gzyl Publisher: World Scientific ISBN: 9814501921 Category : Mathematics Languages : en Pages : 161
Book Description
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.
Author: Jagat Narain Kapur Publisher: John Wiley & Sons ISBN: 9788122402162 Category : Technology & Engineering Languages : en Pages : 660
Book Description
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.
Author: Henryk Gzyl Publisher: Walter de Gruyter GmbH & Co KG ISBN: 3110516136 Category : Mathematics Languages : en Pages : 235
Book Description
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
Author: John Harte Publisher: OUP Oxford ISBN: 0191621161 Category : Science Languages : en Pages : 282
Book Description
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.
Author: Reuven Y. Rubinstein Publisher: Springer Science & Business Media ISBN: 1475743211 Category : Computers Languages : en Pages : 316
Book Description
Rubinstein is the pioneer of the well-known score function and cross-entropy methods. Accessible to a broad audience of engineers, computer scientists, mathematicians, statisticians and in general anyone, theorist and practitioner, who is interested in smart simulation, fast optimization, learning algorithms, and image processing.
Author: Tiziano Squartini Publisher: Springer ISBN: 3319694383 Category : Science Languages : en Pages : 125
Book Description
This book is an introduction to maximum-entropy models of random graphs with given topological properties and their applications. Its original contribution is the reformulation of many seemingly different problems in the study of both real networks and graph theory within the unified framework of maximum entropy. Particular emphasis is put on the detection of structural patterns in real networks, on the reconstruction of the properties of networks from partial information, and on the enumeration and sampling of graphs with given properties. After a first introductory chapter explaining the motivation, focus, aim and message of the book, chapter 2 introduces the formal construction of maximum-entropy ensembles of graphs with local topological constraints. Chapter 3 focuses on the problem of pattern detection in real networks and provides a powerful way to disentangle nontrivial higher-order structural features from those that can be traced back to simpler local constraints. Chapter 4 focuses on the problem of network reconstruction and introduces various advanced techniques to reliably infer the topology of a network from partial local information. Chapter 5 is devoted to the reformulation of certain “hard” combinatorial operations, such as the enumeration and unbiased sampling of graphs with given constraints, within a “softened” maximum-entropy framework. A final chapter offers various overarching remarks and take-home messages.By requiring no prior knowledge of network theory, the book targets a broad audience ranging from PhD students approaching these topics for the first time to senior researchers interested in the application of advanced network techniques to their field.
Author: Adriano Polpo Publisher: Springer ISBN: 9783319911427 Category : Mathematics Languages : en Pages : 304
Book Description
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.
Author: Linghe Kong Publisher: Elsevier ISBN: 012819085X Category : Science Languages : en Pages : 440
Book Description
Big Data in Radio Astronomy: Scientific Data Processing for Advanced Radio Telescopes provides the latest research developments in big data methods and techniques for radio astronomy. Providing examples from such projects as the Square Kilometer Array (SKA), the world's largest radio telescope that generates over an Exabyte of data every day, the book offers solutions for coping with the challenges and opportunities presented by the exponential growth of astronomical data. Presenting state-of-the-art results and research, this book is a timely reference for both practitioners and researchers working in radio astronomy, as well as students looking for a basic understanding of big data in astronomy. - Bridges the gap between radio astronomy and computer science - Includes coverage of the observation lifecycle as well as data collection, processing and analysis - Presents state-of-the-art research and techniques in big data related to radio astronomy - Utilizes real-world examples, such as Square Kilometer Array (SKA) and Five-hundred-meter Aperture Spherical radio Telescope (FAST)
Author: Nailong Wu
Author: Nailong Wu
Author: Henryk Gzyl
Author: John Skilling
Author: Jagat Narain Kapur
Author: Henryk Gzyl
Author: John Harte
Author: Reuven Y. Rubinstein
Author: Tiziano Squartini
Author: Adriano Polpo
Author: Linghe Kong