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Maximum entropy method --- Congresses --- Congresses. --- -519.72 --- Entropy maximization --- Entropy maximum principle --- Maximization, Entropy --- Entropy (Information theory) --- Maximum principles (Mathematics) --- Information theory: mathematical aspects --- Conferences - Meetings --- 519.72 Information theory: mathematical aspects --- 519.72 --- Maximum entropy method - Congresses
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Focusing on Bayesian methods and maximum entropy, this book shows how a few fundamental rules can be used to tackle a variety of problems in data analysis. Topics covered include reliability analysis, multivariate optimisation, least-squares and maximum likelihood, and more.
Maximum entropy method. --- Maximum principles (Mathematics) --- Engineering mathematics. --- Science --- Engineering --- Engineering analysis --- Mathematical analysis --- Differential equations, Partial --- Entropy maximization --- Entropy maximum principle --- Maximization, Entropy --- Entropy (Information theory) --- Mathematics. --- Mathematics --- Numerical solutions
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Non-extensive Entropy Econometrics for Low Frequency Series provides a new and robust power-law-based, non-extensive entropy econometrics approach to the economic modelling of ill-behaved inverse problems. Particular attention is paid to national account-based general equilibrium models known for their relative complexity.In theoretical terms, the approach generalizes Gibbs-Shannon-Golan entropy models, which are useful for describing ergodic phenomena. In essence, this entropy econometrics approach constitutes a junction of two distinct concepts: Jayne's maximum entropy principle and the Bayesian generalized method of moments. Rival econometric techniques are not conceptually adapted to solving complex inverse problems or are seriously limited when it comes to practical implementation. Recent literature showed that amplitude and frequency of macroeconomic fluctuations do not substantially diverge from many other extreme events, natural or human-related, once they are explained in the same time (or space) scale. Non-extensive entropy is a precious device for econometric modelling even in the case of low frequency series, since outputs evolving within the Gaussian attractor correspond to the Tsallis entropy limiting case of Tsallis q-parameter around unity. This book introduces a sub-discipline called Non-extensive Entropy Econometrics or, using a recent expression, Superstar Generalised Econometrics. It demonstrates, using national accounts-based models, that this approach facilitates solving nonlinear, complex inverse problems, previously considered intractable, such as the constant elasticity of substitution class of functions. This new proposed approach could extend the frontier of theoretical and applied econometrics.
Business cycles. --- Econometrics. --- Maximum entropy method. --- generalized cross-entropy, general equilibrium macro-economic model, econometrics. --- BUSINESS & ECONOMICS / Econometrics. --- Entropy maximization --- Entropy maximum principle --- Maximization, Entropy --- Entropy (Information theory) --- Maximum principles (Mathematics) --- Economics, Mathematical --- Statistics --- Economic cycles --- Economic fluctuations --- Cycles
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Ergodic theory. Information theory --- Mathematical distribution theory --- Fourier analysis --- Maximum entropy method --- Positive-definite functions --- Distributions, Positive-definite --- Positive-definite distributions --- Functions --- Entropy maximization --- Entropy maximum principle --- Maximization, Entropy --- Entropy (Information theory) --- Maximum principles (Mathematics) --- Analysis, Fourier --- Mathematical analysis --- Functions, Continuous --- Fonctions continues --- Entropie maximale, Méthode d' --- Fourier, Analyse de --- Fonctions continues. --- Entropie maximale, Méthode d'. --- Fourier, Analyse de.
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Mathematical optimization. --- Maximum entropy method. --- Mathematical optimization --- Optimització matemàtica --- Methodology. --- Mètodes de simulació --- Jocs d'estratègia (Matemàtica) --- Optimització combinatòria --- Programació dinàmica --- Programació (Matemàtica) --- Anàlisi de sistemes --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Entropy maximization --- Entropy maximum principle --- Maximization, Entropy --- Entropy (Information theory) --- Maximum principles (Mathematics)
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The second edition of Introduction to Partial Differential Equations, which originally appeared in the Princeton series Mathematical Notes, serves as a text for mathematics students at the intermediate graduate level. The goal is to acquaint readers with the fundamental classical results of partial differential equations and to guide them into some aspects of the modern theory to the point where they will be equipped to read advanced treatises and research papers. This book includes many more exercises than the first edition, offers a new chapter on pseudodifferential operators, and contains additional material throughout. The first five chapters of the book deal with classical theory: first-order equations, local existence theorems, and an extensive discussion of the fundamental differential equations of mathematical physics. The techniques of modern analysis, such as distributions and Hilbert spaces, are used wherever appropriate to illuminate these long-studied topics. The last three chapters introduce the modern theory: Sobolev spaces, elliptic boundary value problems, and pseudodifferential operators.
Differential equations, Partial. --- Bessel function. --- Cauchy data. --- Dirichlet problem. --- Feynman propagator. --- Gaussian kernel. --- Hadamard example. --- Laplacian. --- Lewy equation. --- Neumann problem. --- Poisson kernel. --- Rellich's theorem. --- Sobolev norm. --- Sobolev space. --- adjoint. --- amplitude. --- cotangent space. --- elliptic operator. --- heat operator. --- maximum principle. --- normal derivative. --- oriented hypersurface. --- parametrix. --- radial function. --- wave operator. --- weak solution.
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Operator theory --- 517.518 --- 51 <082.1> --- Metric theory of functions --- Mathematics--Series --- 517.518 Metric theory of functions --- Interpolation --- Linear operators --- Maximum entropy method --- Interpolation (mathématiques) --- Opérateurs linéaires --- Entropie maximale, Méthode d' --- Opérateurs, Théorie des --- Functional analysis --- Entropy maximization --- Entropy maximum principle --- Maximization, Entropy --- Entropy (Information theory) --- Maximum principles (Mathematics) --- Linear maps --- Maps, Linear --- Operators, Linear --- Approximation theory --- Numerical analysis --- Opérateurs linéaires. --- Entropie maximale, Méthode d'. --- Opérateurs, Théorie des.
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Mathematical statistics --- Quantitative methods (economics) --- Econometrics. --- Maximum entropy method. --- Estimation theory. --- Econométrie --- Théorie de l'estimation --- 330.115 --- Econometrics --- Estimation theory --- Maximum entropy method --- Entropy maximization --- Entropy maximum principle --- Maximization, Entropy --- Entropy (Information theory) --- Maximum principles (Mathematics) --- Estimating techniques --- Least squares --- Stochastic processes --- Economics, Mathematical --- Statistics --- Econometrie --- Social Sciences and Humanities. Economics --- 330.115 Econometrie --- Econométrie --- Théorie de l'estimation --- Économétrie. --- Entropie maximale, Méthode d'. --- Estimation, Théorie de l'. --- Économétrie. --- Entropie maximale, Méthode d'. --- Estimation, Théorie de l'.
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Stochastic processes --- Mathematical statistics --- Bayesian statistical decision theory --- Maximum entropy method --- Bayesian statistical decision theory. --- Maximum entropy method. --- Statistique bayésienne --- Entropie maximale, Méthode d' --- 519.5 --- Entropy maximization --- Entropy maximum principle --- Maximization, Entropy --- Entropy (Information theory) --- Maximum principles (Mathematics) --- Bayes' solution --- Bayesian analysis --- Statistical decision --- Engineering mathematics --- Science --- Principes du maximum (Mathématiques) --- Mathématiques de l'ingénieur --- Sciences --- Mathematics --- Mathématiques --- Statistique bayésienne. --- Entropie maximale, Méthode d'. --- 519.24 --- 519.24 Special statistical applications and models --- Special statistical applications and models --- Statistique bayésienne. --- Entropie maximale, Méthode d'.
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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.
Physics. --- System theory. --- Graph theory. --- Complexity, Computational. --- Applications of Graph Theory and Complex Networks. --- Statistical Physics and Dynamical Systems. --- Complex Systems. --- Graph Theory. --- Complexity. --- Maximum entropy method. --- Entropy maximization --- Entropy maximum principle --- Maximization, Entropy --- Entropy (Information theory) --- Maximum principles (Mathematics) --- Statistical physics. --- Engineering. --- Construction --- Industrial arts --- Technology --- Physics --- Mathematical statistics --- Statistical methods --- Computational complexity. --- Complexity, Computational --- Electronic data processing --- Machine theory --- Graph theory --- Graphs, Theory of --- Theory of graphs --- Combinatorial analysis --- Topology --- Systems, Theory of --- Systems science --- Science --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Extremal problems --- Philosophy
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