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Sunday, April 26, 2020 | History

4 edition of Information and exponential families found in the catalog.

Information and exponential families

O. E. Barndorff-Nielsen

Information and exponential families

in statistical theory

by O. E. Barndorff-Nielsen

  • 38 Want to read
  • 24 Currently reading

Published by Wiley in Chichester, New York .
Written in English

    Subjects:
  • Sufficient statistics.,
  • Distribution (Probability theory),
  • Exponential functions.

  • Edition Notes

    Includes bibliographical references and index.

    StatementO. Barndorff-Nielsen.
    SeriesWiley series in probability and mathematical statistics.
    Classifications
    LC ClassificationsQA276 .B2847
    The Physical Object
    Paginationix, 238 p. :
    Number of Pages238
    ID Numbers
    Open LibraryOL4542823M
    ISBN 100471995452
    LC Control Number77009943

    This book is a readable, digestible introduction to exponential families, encompassing statistical models based on the most useful distributions in statistical theory, such as the normal, gamma, binomial, Poisson, and negative binomial. Strongly motivated by applications, it presents the essential theory and then demonstrates the theory’s. The exponential family just defined includes as special cases the normal, binomial, Poisson, exponential, gamma and inverse Gaussian distributions. Example: The normal distribution has density f(y i) = 1 √ 2πσ2 exp{− 1 2 (y i −µ i)2 σ2}. Expanding the square in the exponent we get (y i − µ i)2 = y2 i + µ2i − 2y iµ i, so the File Size: KB. This monograph presents a systematic treatment of the analytical an probabilistic properties of exponential families.


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Information and exponential families by O. E. Barndorff-Nielsen Download PDF EPUB FB2

Information and Exponential Families: In Statistical Theory (Wiley Series in Probability and Statistics) 2nd Edition by O. Barndorff-Nielsen (Author) ISBN ISBN Why is ISBN important.

ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book. Cited by:   Information and Exponential Families: In Statistical Theory. Author(s): O. Barndorff‐Nielsen; 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. The book is an excellent introduction to the fundamental properties of statistical exponential families and a natural starting point.

If you buy one book on statistical exponential families, buy Barndorff-Nielsen. The book may be hard to read, but it is to the point. It is rewarding and deeply satisfying.2/5(2). The book presents a general treatment of the topics of statistical information, and develops the theory of exponential families.

Properties of convex sets and functions, in particular convex duality relations, are of great importance for the study of exponential families.

First published by Wiley inthis 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 authors selection of topics.

His treatise brings together results on aspects of statistical information, notably. First published by Wiley inthis 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.

Open Library is an open, editable library catalog, building towards a web page for every book ever published. Information and exponential families by O. Barndorff-Nielsen,Wiley edition, in EnglishCited by: COVID Resources.

Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.

Information and Exponential Families: In Statisical Theory Wiley Series in Probability and Mathematical Statistics Series Wiley series in probability and mathematical statistics. Probability and mathematical statistics: Author: Ole Barndorff-Nielsen: Edition: illustrated: Publisher: J.

Wiley, In the modern setting, information geometry applies to a much wider context, including non-exponential families, nonparametric statistics, and even abstract statistical manifolds not induced from a known statistical model.

The results combine techniques from information theory, affine differential geometry, convex analysis and many other fields. Request PDF | Information and Exponential Families in Statistical Theory | First published by Wiley inthis book is being re-issued with a new Preface by the author.

The roots of the book Author: Ole Eiler Barndorff-Nielsen. Robert L. Devaney, in Handbook of Dynamical Systems, Explosions.

The complex exponential family has only one singular value, namely the asymptotic value at 0. Just as in the quadratic case, we use the orbit of this point to paint the picture of the parameter plane for E do not get as sharp a dichotomy in the exponential case, as the topology of the Julia sets for E λ do not.

of Fisher information. These smoothness conditions hold for exponential families, so at least in the exponential family case, everything in this chapter is rigorous. (We note in passing that there are more general definitions of Fisher information for more general families under quadratic mean differentiability; see, for example, van der.

exponential family. Accordingly, Section 3 is devoted to a discussion of exponential families, focusing on the mathematical links to convex analysis, and thus anticipating our development of variational meth-ods.

In particular, the principal object of interest in our exposition is a certain conjugate dual relation associated with exponential. Book Source: Digital Library of India Item : O B ioned: ble. Working with exponential family representations, and exploiting the conjugate duality between the cumulant function and the entropy for exponential families, Graphical Models, Exponential Families and Variational Inference develops general variational representations of the problems of computing likelihoods, marginal probabilities and most.

Exponential Families at the Singularity University Global Summit. Exponential Families is a unique experience at the Singularity University Global Summit that has been custom designed for leading families.

Families will have VIP access to the entire conference, plus Exponential Families attendees will have private Q&A sessions with select Summit speakers.

2 CHAPTER 8. THE EXPONENTIAL FAMILY: BASICS where we see that the cumulant function can be viewed as the logarithm of a normalization factor.1 This shows that A(η) is not a degree of freedom in the specification of an exponential family density; it is determined once ν, T(x) and h(x) are determined.2 The set of parameters ηfor which the integral in Size: KB.

Statistical Estimation for Truncated Exponential Families. Authors: Akahira, Masafumi This book presents new findings on nonregular statistical estimation. Unlike other books on this topic, its major emphasis is on helping readers understand the meaning and implications of both regularity and irregularity through a certain family of Brand: Springer Singapore.

In this book, the authors present the newly developed theory of non-harmonic Fourier series and its applications to the control of distributed parameter systems, and they extend the theory to include vector exponential series.

The first part of the book presents the modern theory of exponentials, using an operator theory approach. The second extends and upgrades the method of moments--one of. Maximum Entropy and Exponential Families April 9, Abstract The goal of this note is to derive the exponential form of probability distribution from more basic considerations, in particular Entropy.

It follows a description by ET Jaynes in Chapter 11 of his book Probability Theory: the Logic of Science [1].1 1 Motivating the Exponential ModelFile Size: KB. This book is a readable, digestible introduction to exponential families, encompassing statistical models based on the most useful distributions in statistical theory, including the normal, gamma, binomial, Poisson, and negative binomial.

Strongly motivated by applications, it presents the essential theory and then demonstrates the theory's Cited by: 1. On Information Closures of Exponential Families: A Counterexample Article in IEEE Transactions on Information Theory 50(5) June with 9 Reads How we measure 'reads'. First published by Wiley inthis 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 : O Barndorff-Nielsen.

Examples include the binomial, Poisson, normal, exponential, geometric, and other distributions in regular use. From a theoretical perspective, exponential families are quite regular. In addition, moments for these distributions can often be computed easily using the differential identities in. From (13) we can see that exponential families are closed under independent, indentically distributed sampling, and that the minimal sufficient statistic for θ is the k-dimensional vector T=Σt(Y i).Exponential families are said to permit a sufficiency reduction under sampling; we can replace the original n observations by a vector of length k.

Exponential Families is a VIP experience at the Singularity University Global Summit that has been custom designed for families. Families will have VIP access to the entire conference, which you can learn about here, plus Exponential Families attendees will have private Q&A sessions with select Summit speakers, including.

Graphical Models, Exponential Families, and Variational Inference book. Read reviews from world’s largest community for readers. The formalism of probabi /5. INFORMATION AND EXPONENTIAL FAMILIES in Statistical Theory by 0. Barndorff-Nielsen, Mathematical Institute, Aarhus University, Denmark.

In the theory of statistics, information is embodied in probability functions, likelihood and plausibility functions, and predictiori functions.

Relative to any particular question, part of the. Alexander J. Smola: Exponential Families and Kernels, Page 24 Entropy Basically it’s the number of bits needed to encode a ran-dom variable.

It is defined as H(p) = Z −p(x)logp(x)dx where we set 0log0:= 0 Maximum Entropy Density The density p(x) satisfying E[φ(x)] ≥ η with maximum entropy is exp(hφ(x),θi−g(θ)). Corollary. Graphical Models, Exponential Families, and Variational Inference (Foundations and Trends(r) Machine Learning) and a great selection of related books, art and collectibles available now at The Exponential Family of Distributions p(x)=h(x)eµ>T(x)¡A(µ) To get a normalized distribution, for any µ Z p(x)dx=e¡A(µ) Z h(x)eµ>T(x)dx=1 so eA(µ)= Z h(x)eµ>T(x)dx; i.e., when T(x)=x, A(µ)is the logof Laplace transform of h(x).File Size: 61KB.

Graphical Models, Exponential Families, and Variational Inference Martin J. Wainwright, Department of Statistics, and Department of Electrical Engineering and Computer Science, University of California, USA, [email protected] Michael I.

Jordan, Department of Statistics, and Department of Electrical Engineering and Computer Science, University of California, USA, [email protected] by: Statistical Modelling by Exponential Families.

Journal of the American Statistical Association. Accepted. 3) exponential decay function 2) linear function with a positive rate of change 4) exponential growth function.

) Rachel and Marc were given the information shown below about the bacteria growing in a Petri dish in their biology class. Rachel wants to model this information with a linear function. Marc wants to use an exponential Size: KB. Hessian structures and divergence functions on deformed exponential families.- Harmonic maps relative to alpha-connections.- A Riemannian geometry in the q-exponential Banach manifold induced by q-divergences.- Computational algebraic methods in efficient estimation.

(source: Nielsen Book. 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.

Exponential Families of Stochastic Processes - Ebook written by Uwe Küchler, Michael Sorensen. Read this book using Google Play Books app on your PC, android, iOS devices.

Download for offline reading, highlight, bookmark or take notes while. Infinite-Dimensional Exponential Families Posted by David Corfield. Back on my old blog I posted a few times on information geometry (1, 2, 3, 4).One key idea is the duality between projecting from a prior distribution onto the manifold of distributions, a specified set of whose moments match those of the empirical distribution, and projecting from the empirical distribution onto the.

Abstract. Morris’ paper has distinctly two parts: the first one sets the stage for natural exponential families, or NEF (Sections 1, 2, 7, 9, and 10); the other one concentrates on NEF with quadratic variance functions, called QVF by by: 2.

Here, we show that there exists another duality that arises in the context of information geometry, relating the Fisher information of ϕ -deformed exponential families that correspond to linear constraints (as studied by ) to those that are based on escort constraints (as studied by S.-I.

Amari).Cited by: 3. Information Theory and Statistics. 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 Cited by:   Underlying information geometry is the question of what it means to put a geometry on a set of probability distributions.

Ultimately, we will be viewing sets of probability distributions as manifolds with metrics and connections having statistical relevance. (Metrics and connections are Riemannian geometric concepts determining, among other things, how distance is measured and what.