The Method of Maximum Entropy

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 app

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

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.

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 applicatio

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.

In the theory and practice of econometrics the model, the method and the data are all interdependent links in information recovery-estimation and inference. Seldom, however, are the economic and stati

For over 30 years, the MaxEnt workshops have explored Bayesian and Maximum Entropymethods in scientific, engineering, and signal processing applications. This proceedings volume covers all aspects of

MaxEnt workshops are devoted to Bayesian inference and Maximum Entropy methods in sciences and engineering. This year's meeting was also encompassed all aspects of probabilistic inference such as foun

The MaxEnt2008 - 28th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering - encompassed all aspects of information theory, probability, statistical infe

This excellent volume considers the methods, applications and even the foundations of a key area of theoretical study. Namely, that of Bayesian probability, entropy and information theory in scientifi

The global biodiversity crisis is one of humanity's most urgent problems, but even quantifying biological diversity is a difficult mathematical and conceptual challenge. This book brings new mathematical rigour to the ongoing debate. It was born of research in category theory, is given strength by information theory, and is fed by the ancient field of functional equations. It applies the power of the axiomatic method to a biological problem of pressing concern, but it also presents new theorems that stand up as mathematics in their own right, independently of any application. The question 'what is diversity?' has surprising mathematical depth, and this book covers a wide breadth of mathematics, from functional equations to geometric measure theory, from probability theory to number theory. Despite this range, the mathematical prerequisites are few: the main narrative thread of this book requires no more than an undergraduate course in analysis.

The global biodiversity crisis is one of humanity's most urgent problems, but even quantifying biological diversity is a difficult mathematical and conceptual challenge. This book brings new mathematical rigour to the ongoing debate. It was born of research in category theory, is given strength by information theory, and is fed by the ancient field of functional equations. It applies the power of the axiomatic method to a biological problem of pressing concern, but it also presents new theorems that stand up as mathematics in their own right, independently of any application. The question 'what is diversity?' has surprising mathematical depth, and this book covers a wide breadth of mathematics, from functional equations to geometric measure theory, from probability theory to number theory. Despite this range, the mathematical prerequisites are few: the main narrative thread of this book requires no more than an undergraduate course in analysis.

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 anyo

The advent of electronic computing permits the empirical analysis of economic models of far greater subtlety and rigour than before, when many interesting ideas were not followed up because the calculations involved made this impracticable. The estimation and testing of these more intricate models is usually based on the method of Maximum Likelihood, which is a well-established branch of mathematical statistics. Its use in econometrics has led to the development of a number of special techniques; the specific conditions of econometric research moreover demand certain changes in the interpretation of the basic argument. This book is a self-contained introduction to this field. It consists of three parts. The first deals with general features of Maximum Likelihood methods; the second with linear and nonlinear regression; and the third with discrete choice and related micro-economic models. Readers should already be familiar with elementary statistical theory, with applied econometric res

This volume provides a practical introduction to the method of maximum likelihood as used in social science research. Ward and Ahlquist focus on applied computation in R and use real social science data from actual, published research. Unique among books at this level, it develops simulation-based tools for model evaluation and selection alongside statistical inference. The book covers standard models for categorical data as well as counts, duration data, and strategies for dealing with data missingness. By working through examples, math, and code, the authors build an understanding about the contexts in which maximum likelihood methods are useful and develop skills in translating mathematical statements into executable computer code. Readers will not only be taught to use likelihood-based tools and generate meaningful interpretations, but they will also acquire a solid foundation for continued study of more advanced statistical techniques.

A revolutionary method of weight lifting using today's science for maximum results. In The New Rules of Lifting, fitness guru Lou Schuler and strength-training expert Alwyn Cosgrove boil down the mo

This volume provides a practical introduction to the method of maximum likelihood as used in social science research. Ward and Ahlquist focus on applied computation in R and use real social science data from actual, published research. Unique among books at this level, it develops simulation-based tools for model evaluation and selection alongside statistical inference. The book covers standard models for categorical data as well as counts, duration data, and strategies for dealing with data missingness. By working through examples, math, and code, the authors build an understanding about the contexts in which maximum likelihood methods are useful and develop skills in translating mathematical statements into executable computer code. Readers will not only be taught to use likelihood-based tools and generate meaningful interpretations, but they will also acquire a solid foundation for continued study of more advanced statistical techniques.

Like all previous MaxEnt Workshops, this meeting encompassed all aspects of probabilistic inference including foundations, computational methods, and applications. The topics represented included prob

A multitude of processes in hydrology and environmental engineering are either random or entail random components which are characterized by random variables. These variables are described by frequency distributions. This book provides an overview of different systems of frequency distributions, their properties, and applications to the fields of water resources and environmental engineering. A variety of systems are covered, including the Pearson system, Burr system, and systems commonly applied in economics, such as the D'Addario, Dagum, Stoppa, and Esteban systems. The latter chapters focus on the Singh system and the frequency distributions deduced from Bessel functions, maximum entropy theory, and the transformations of random variables. The final chapter introduces the genetic theory of frequency distributions. Using real-world data, this book provides a valuable reference for researchers, graduate students, and professionals interested in frequency analysis.

A multitude of processes in hydrology and environmental engineering are either random or entail random components which are characterized by random variables. These variables are described by frequency distributions. This book provides an overview of different systems of frequency distributions, their properties, and applications to the fields of water resources and environmental engineering. A variety of systems are covered, including the Pearson system, Burr system, and systems commonly applied in economics, such as the D'Addario, Dagum, Stoppa, and Esteban systems. The latter chapters focus on the Singh system and the frequency distributions deduced from Bessel functions, maximum entropy theory, and the transformations of random variables. The final chapter introduces the genetic theory of frequency distributions. Using real-world data, this book provides a valuable reference for researchers, graduate students, and professionals interested in frequency analysis.

CRITS: A Student Manual is a practical guide to help art and design students obtain maximum benefits from the most common method of teaching these subjects in college: the studio critique. CRITS posit

CRITS: A Student Manual is a practical guide to help art and design students obtain maximum benefits from the most common method of teaching these subjects in college: the studio critique. CRITS posit

This book presents a systematic explanation of the SIML (Separating Information Maximum Likelihood) method, a new approach to financial econometrics.Considerable interest has been given to the estimat

This thesis presents a pioneering method for gleaning the maximum information from the deepest images of the far-infrared universe obtained with the Herschel satellite, reaching galaxies fainter by an

Optimization is used to determine the most appropriate value of variables under given conditions. The primary focus of using optimisation techniques is to measure the maximum or minimum value of a function depending on the circumstances. This book discusses problem formulation and problem solving with the help of algorithms such as secant method, quasi-Newton method, linear programming and dynamic programming. It also explains important chemical processes such as fluid flow systems, heat exchangers, chemical reactors and distillation systems using solved examples. The book begins by explaining the fundamental concepts followed by an elucidation of various modern techniques including trust-region methods, Levenberg–Marquardt algorithms, stochastic optimization, simulated annealing and statistical optimization. It studies the multi-objective optimization technique and its applications in chemical engineering and also discusses the theory and applications of various optimization software

Computing is revolutionizing the practice of biology. This book, which assumes no prior computing experience, provides students with the tools to write their own Python programs and to understand fundamental concepts in computational biology and bioinformatics. Each major part of the book begins with a compelling biological question, followed by the algorithmic ideas and programming tools necessary to explore it: the origins of pathogenicity are examined using gene finding, the evolutionary history of sex determination systems is studied using sequence alignment, and the origin of modern humans is addressed using phylogenetic methods. In addition to providing general programming skills, this book explores the design of efficient algorithms, simulation, NP-hardness, and the maximum likelihood method, among other key concepts and methods. Easy-to-read and designed to equip students with the skills to write programs for solving a range of biological problems, the book is accompanied by nu

Computing is revolutionizing the practice of biology. This book, which assumes no prior computing experience, provides students with the tools to write their own Python programs and to understand fundamental concepts in computational biology and bioinformatics. Each major part of the book begins with a compelling biological question, followed by the algorithmic ideas and programming tools necessary to explore it: the origins of pathogenicity are examined using gene finding, the evolutionary history of sex determination systems is studied using sequence alignment, and the origin of modern humans is addressed using phylogenetic methods. In addition to providing general programming skills, this book explores the design of efficient algorithms, simulation, NP-hardness, and the maximum likelihood method, among other key concepts and methods. Easy-to-read and designed to equip students with the skills to write programs for solving a range of biological problems, the book is accompanied by nu

From the basics to the forefront of modern research, this book presents all aspects of probability theory, statistics and data analysis from a Bayesian perspective for physicists and engineers. The book presents the roots, applications and numerical implementation of probability theory, and covers advanced topics such as maximum entropy distributions, stochastic processes, parameter estimation, model selection, hypothesis testing and experimental design. In addition, it explores state-of-the art numerical techniques required to solve demanding real-world problems. The book is ideal for students and researchers in physical sciences and engineering.

The author develops a novel analysis method for QCD sum rules (QCDSR) by applying the maximum entropy method (MEM) to arrive at an analysis with less artificial assumptions than previously held. This

This book provides a general framework for specifying, estimating and testing time series econometric models. Special emphasis is given to estimation by maximum likelihood, but other methods are also discussed, including quasi-maximum likelihood estimation, generalised method of moments estimation, nonparametric estimation and estimation by simulation. An important advantage of adopting the principle of maximum likelihood as the unifying framework for the book is that many of the estimators and test statistics proposed in econometrics can be derived within a likelihood framework, thereby providing a coherent vehicle for understanding their properties and interrelationships. In contrast to many existing econometric textbooks, which deal mainly with the theoretical properties of estimators and test statistics through a theorem-proof presentation, this book squarely addresses implementation to provide direct conduits between the theory and applied work.

This book provides a general framework for specifying, estimating and testing time series econometric models. Special emphasis is given to estimation by maximum likelihood, but other methods are also discussed, including quasi-maximum likelihood estimation, generalised method of moments estimation, nonparametric estimation and estimation by simulation. An important advantage of adopting the principle of maximum likelihood as the unifying framework for the book is that many of the estimators and test statistics proposed in econometrics can be derived within a likelihood framework, thereby providing a coherent vehicle for understanding their properties and interrelationships. In contrast to many existing econometric textbooks, which deal mainly with the theoretical properties of estimators and test statistics through a theorem-proof presentation, this book squarely addresses implementation to provide direct conduits between the theory and applied work.

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 o

Plant community ecology has traditionally taken a taxonomical approach based on population dynamics. This book contrasts such an approach with a trait-based approach. After reviewing these two approaches, it then explains how models based on the Maximum Entropy Formalism can be used to predict the relative abundance of different species from a potential species pool. Following this it shows how the trait constraints, upon which the model is based, are necessary consequences of natural selection and population dynamics. The final sections of the book extend the discussion to macroecological patterns of species abundance and concludes with some outstanding unresolved questions. Written for advanced undergraduates, graduates and researchers in plant ecology, Bill Shipley demonstrates how a trait-based approach, can explain how the principle of natural selection and quantitative genetics can be combined with maximum entropy methods to explain and predict the structure of plant communities.

Plant community ecology has traditionally taken a taxonomical approach based on population dynamics. This book contrasts such an approach with a trait-based approach. After reviewing these two approaches, it then explains how models based on the Maximum Entropy Formalism can be used to predict the relative abundance of different species from a potential species pool. Following this it shows how the trait constraints, upon which the model is based, are necessary consequences of natural selection and population dynamics. The final sections of the book extend the discussion to macroecological patterns of species abundance and concludes with some outstanding unresolved questions. Written for advanced undergraduates, graduates and researchers in plant ecology, Bill Shipley demonstrates how a trait-based approach, can explain how the principle of natural selection and quantitative genetics can be combined with maximum entropy methods to explain and predict the structure of plant communities.

This book was first published in 1995. The problem of disparities between different estimates of GDP is well known and widely discussed. Here, the authors describe a method for examining the discrepancies using a technique allocating them with reference to data reliability. The method enhances the reliability of the underlying data and leads to maximum-likelihood estimates. It is illustrated by application to the UK national accounts for the period 1920–1990. The book includes a full set of estimates for this period, including runs of industrial data for the period 1948–1990, which are longer than those available from any other source. The statistical technique allows estimates of standard errors of the data to be calculated and verified; these are presented both for data in levels and for changes in variables over 1-, 2- and 5-year periods.

This book presents a theoretical treatment of nonlinear behaviour of solids and structures in such a way that it is suitable for numerical computation, typically using the Finite Element Method. Starting out from elementary concepts, the author systematically uses the principle of virtual work, initially illustrated by truss structures, to give a self-contained and rigorous account of the basic methods. The author illustrates the combination of translations and rotations by finite deformation beam theories in absolute and co-rotation format, and describes the deformation of a three-dimensional continuum in material form. A concise introduction to finite elasticity is followed by an extension to elasto-plastic materials via internal variables and the maximum dissipation principle. Finally, the author presents numerical techniques for solution of the nonlinear global equations and summarises recent results on momentum and energy conserving integration of time-dependent problems. Exercise

This updated textbook is an excellent way to introduce probability and information theory to new students in mathematics, computer science, engineering, statistics, economics, or business studies. Only requiring knowledge of basic calculus, it starts by building a clear and systematic foundation to the subject: the concept of probability is given particular attention via a simplified discussion of measures on Boolean algebras. The theoretical ideas are then applied to practical areas such as statistical inference, random walks, statistical mechanics and communications modelling. Topics covered include discrete and continuous random variables, entropy and mutual information, maximum entropy methods, the central limit theorem and the coding and transmission of information, and added for this new edition is material on Markov chains and their entropy. Lots of examples and exercises are included to illustrate how to use the theory in a wide range of applications, with detailed solutions to

This updated textbook is an excellent way to introduce probability and information theory to new students in mathematics, computer science, engineering, statistics, economics, or business studies. Only requiring knowledge of basic calculus, it starts by building a clear and systematic foundation to the subject: the concept of probability is given particular attention via a simplified discussion of measures on Boolean algebras. The theoretical ideas are then applied to practical areas such as statistical inference, random walks, statistical mechanics and communications modelling. Topics covered include discrete and continuous random variables, entropy and mutual information, maximum entropy methods, the central limit theorem and the coding and transmission of information, and added for this new edition is material on Markov chains and their entropy. Lots of examples and exercises are included to illustrate how to use the theory in a wide range of applications, with detailed solutions to

Hamilton's Ricci flow has attracted considerable attention since its introduction in 1982, owing partly to its promise in addressing the Poincaré conjecture and Thurston's geometrization conjecture. This book gives a concise introduction to the subject with the hindsight of Perelman's breakthroughs from 2002/2003. After describing the basic properties of, and intuition behind the Ricci flow, core elements of the theory are discussed such as consequences of various forms of maximum principle, issues related to existence theory, and basic properties of singularities in the flow. A detailed exposition of Perelman's entropy functionals is combined with a description of Cheeger-Gromov-Hamilton compactness of manifolds and flows to show how a 'tangent' flow can be extracted from a singular Ricci flow. Finally, all these threads are pulled together to give a modern proof of Hamilton's theorem that a closed three-dimensional manifold whichcarries a metric of positive Ricci curvature is a spher