Information And Exponential Families

Author : O. Barndorff-Nielsen
Publisher : John Wiley & Sons
Page : 248 pages
File Size : 44,9 Mb
Release : 2014-05-07
Category : Mathematics
ISBN : 9781118857373

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Information and Exponential Families by O. Barndorff-Nielsen Pdf

First published by Wiley in 1978, this book is being re-issued with a new Preface by the author. The roots of the book lie in the writings of RA Fisher both as concerns results and the general stance to statistical science, and this stance was the determining factor in the author's selection of topics. His treatise brings together results on aspects of statistical information, notably concerning likelihood functions, plausibility functions, ancillarity, and sufficiency, and on exponential families of probability distributions.

Author : Ole E. Barndorff-Nielsen
Publisher : Unknown
Page : 238 pages
File Size : 43,9 Mb
Release : 1978
Category : Distribution (Probability theory)
ISBN : OCLC:30398003

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Information and Exponential Families by Ole E. Barndorff-Nielsen Pdf

Author : Ole Barndorff-Nielsen
Publisher : Unknown
Page : 238 pages
File Size : 41,6 Mb
Release : 1978
Category : Electronic
ISBN : 0835733912

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Information and Exponential Families by Ole Barndorff-Nielsen Pdf

Author : Uwe Küchler,Michael Sorensen
Publisher : Springer Science & Business Media
Page : 322 pages
File Size : 40,6 Mb
Release : 2006-05-09
Category : Mathematics
ISBN : 9780387227658

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Exponential Families of Stochastic Processes by Uwe Küchler,Michael Sorensen Pdf

A comprehensive account of the statistical theory of exponential families of stochastic processes. The book reviews the progress in the field made over the last ten years or so by the authors - two of the leading experts in the field - and several other researchers. The theory is applied to a broad spectrum of examples, covering a large number of frequently applied stochastic process models with discrete as well as continuous time. To make the reading even easier for statisticians with only a basic background in the theory of stochastic process, the first part of the book is based on classical theory of stochastic processes only, while stochastic calculus is used later. Most of the concepts and tools from stochastic calculus needed when working with inference for stochastic processes are introduced and explained without proof in an appendix. This appendix can also be used independently as an introduction to stochastic calculus for statisticians. Numerous exercises are also included.

Author : Stefan Bedbur,Udo Kamps
Publisher : Springer Nature
Page : 147 pages
File Size : 51,6 Mb
Release : 2021-10-07
Category : Mathematics
ISBN : 9783030819002

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Multivariate Exponential Families: A Concise Guide to Statistical Inference by Stefan Bedbur,Udo Kamps Pdf

This book provides a concise introduction to exponential families. Parametric families of probability distributions and their properties are extensively studied in the literature on statistical modeling and inference. Exponential families of distributions comprise density functions of a particular form, which enables general assertions and leads to nice features. With a focus on parameter estimation and hypotheses testing, the text introduces the reader to distributional and statistical properties of multivariate and multiparameter exponential families along with a variety of detailed examples. The material is widely self-contained and written in a mathematical setting. It may serve both as a concise, mathematically rigorous course on exponential families in a systematic structure and as an introduction to Mathematical Statistics restricted to the use of exponential families.

Author : Lawrence D. Brown
Publisher : IMS
Page : 302 pages
File Size : 42,6 Mb
Release : 1986
Category : Business & Economics
ISBN : 0940600102

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Fundamentals of Statistical Exponential Families by Lawrence D. Brown Pdf

Author : Martin J. Wainwright,Michael Irwin Jordan
Publisher : Now Publishers Inc
Page : 324 pages
File Size : 45,7 Mb
Release : 2008
Category : Computers
ISBN : 9781601981844

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Graphical Models, Exponential Families, and Variational Inference by Martin J. Wainwright,Michael Irwin Jordan Pdf

The core of this paper is a general set of variational principles for the problems of computing marginal probabilities and modes, applicable to multivariate statistical models in the exponential family.

Author : Rolf Sundberg
Publisher : Cambridge University Press
Page : 297 pages
File Size : 45,8 Mb
Release : 2019-08-29
Category : Business & Economics
ISBN : 9781108476591

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Statistical Modelling by Exponential Families by Rolf Sundberg Pdf

A readable, digestible introduction to essential theory and wealth of applications, with a vast set of examples and numerous exercises.

Author : Bo-Cheng Wei
Publisher : Unknown
Page : 248 pages
File Size : 52,9 Mb
Release : 1998-09
Category : Mathematics
ISBN : UOM:39015043239618

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Exponential Family Nonlinear Models by Bo-Cheng Wei Pdf

This book gives a comprehensive introduction to exponential family nonlinear models, which are the natural extension of generalized linear models and normal nonlinear regression models. The differential geometric framework is presented for these models and geometric methods are widely used in this book. This book is ideally suited for researchers in statistical interfaces and graduate students with a basic knowledge of statistics.

Author : Gary A. Simon,Stanford University. Department of Statistics
Publisher : Unknown
Page : 350 pages
File Size : 43,5 Mb
Release : 1971
Category : Information theory
ISBN : STANFORD:36105025648515

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Information Distances and Exponential Families, with Applications to Contingency Tables by Gary A. Simon,Stanford University. Department of Statistics Pdf

Author : Imre Csiszár,Paul C. Shields
Publisher : Now Publishers Inc
Page : 128 pages
File Size : 45,6 Mb
Release : 2004
Category : Computers
ISBN : 1933019050

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Information Theory and Statistics by Imre Csiszár,Paul C. Shields Pdf

Information Theory and Statistics: A Tutorial is concerned with applications of information theory concepts in statistics, in the finite alphabet setting. The topics covered include large deviations, hypothesis testing, maximum likelihood estimation in exponential families, analysis of contingency tables, and iterative algorithms with an "information geometry" background. Also, an introduction is provided to the theory of universal coding, and to statistical inference via the minimum description length principle motivated by that theory. The tutorial does not assume the reader has an in-depth knowledge of Information Theory or statistics. As such, Information Theory and Statistics: A Tutorial, is an excellent introductory text to this highly-important topic in mathematics, computer science and electrical engineering. It provides both students and researchers with an invaluable resource to quickly get up to speed in the field.

Author : Shuguang Cui,Alfred O. Hero, III,Zhi-Quan Luo,José M. F. Moura
Publisher : Cambridge University Press
Page : 459 pages
File Size : 48,7 Mb
Release : 2016-01-14
Category : Computers
ISBN : 9781107099005

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Big Data over Networks by Shuguang Cui,Alfred O. Hero, III,Zhi-Quan Luo,José M. F. Moura Pdf

Examines the crucial interaction between big data and communication, social and biological networks using critical mathematical tools and state-of-the-art research.

Author : Frank Nielsen,Frédéric Barbaresco
Publisher : Springer Nature
Page : 929 pages
File Size : 53,7 Mb
Release : 2021-07-14
Category : Computers
ISBN : 9783030802097

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Geometric Science of Information by Frank Nielsen,Frédéric Barbaresco Pdf

This book constitutes the proceedings of the 5th International Conference on Geometric Science of Information, GSI 2021, held in Paris, France, in July 2021. The 98 papers presented in this volume were carefully reviewed and selected from 125 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: Probability and statistics on Riemannian Manifolds; sub-Riemannian geometry and neuromathematics; shapes spaces; geometry of quantum states; geometric and structure preserving discretizations; information geometry in physics; Lie group machine learning; geometric and symplectic methods for hydrodynamical models; harmonic analysis on Lie groups; statistical manifold and Hessian information geometry; geometric mechanics; deformed entropy, cross-entropy, and relative entropy; transformation information geometry; statistics, information and topology; geometric deep learning; topological and geometrical structures in neurosciences; computational information geometry; manifold and optimization; divergence statistics; optimal transport and learning; and geometric structures in thermodynamics and statistical physics.

Author : Bradley Efron
Publisher : Cambridge University Press
Page : 264 pages
File Size : 53,7 Mb
Release : 2022-12-15
Category : Mathematics
ISBN : 9781108805438

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Exponential Families in Theory and Practice by Bradley Efron Pdf

During the past half-century, exponential families have attained a position at the center of parametric statistical inference. Theoretical advances have been matched, and more than matched, in the world of applications, where logistic regression by itself has become the go-to methodology in medical statistics, computer-based prediction algorithms, and the social sciences. This book is based on a one-semester graduate course for first year Ph.D. and advanced master's students. After presenting the basic structure of univariate and multivariate exponential families, their application to generalized linear models including logistic and Poisson regression is described in detail, emphasizing geometrical ideas, computational practice, and the analogy with ordinary linear regression. Connections are made with a variety of current statistical methodologies: missing data, survival analysis and proportional hazards, false discovery rates, bootstrapping, and empirical Bayes analysis. The book connects exponential family theory with its applications in a way that doesn't require advanced mathematical preparation.

Author : David J. Olive
Publisher : Springer
Page : 434 pages
File Size : 41,6 Mb
Release : 2014-05-07
Category : Mathematics
ISBN : 9783319049724

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Statistical Theory and Inference by David J. Olive Pdf

This text is for a one semester graduate course in statistical theory and covers minimal and complete sufficient statistics, maximum likelihood estimators, method of moments, bias and mean square error, uniform minimum variance estimators and the Cramer-Rao lower bound, an introduction to large sample theory, likelihood ratio tests and uniformly most powerful tests and the Neyman Pearson Lemma. A major goal of this text is to make these topics much more accessible to students by using the theory of exponential families. Exponential families, indicator functions and the support of the distribution are used throughout the text to simplify the theory. More than 50 ``brand name" distributions are used to illustrate the theory with many examples of exponential families, maximum likelihood estimators and uniformly minimum variance unbiased estimators. There are many homework problems with over 30 pages of solutions.