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Author: O. Barndorff-Nielsen
Publisher: John Wiley & Sons
ISBN: 1118857372
Category : Mathematics
Languages : en
Pages : 248
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Book Description
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: O. Barndorff-Nielsen
Publisher: John Wiley & Sons
ISBN: 1118857372
Category : Mathematics
Languages : en
Pages : 248
Get Book
Book Description
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:
ISBN:
Category : Distribution (Probability theory)
Languages : en
Pages : 238
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Book Description
Author: Uwe Küchler
Publisher: Springer Science & Business Media
ISBN: 0387227652
Category : Mathematics
Languages : en
Pages : 322
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Book Description
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: Lawrence D. Brown
Publisher: IMS
ISBN: 9780940600102
Category : Business & Economics
Languages : en
Pages : 302
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Book Description
Author: Stefan Bedbur
Publisher: Springer Nature
ISBN: 3030819000
Category : Mathematics
Languages : en
Pages : 147
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Book Description
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: Martin J. Wainwright
Publisher: Now Publishers Inc
ISBN: 1601981848
Category : Computers
Languages : en
Pages : 324
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Book Description
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: Ole Barndorff-Nielsen
Publisher:
ISBN: 9780835733915
Category :
Languages : en
Pages : 238
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Book Description
Author: Rolf Sundberg
Publisher: Cambridge University Press
ISBN: 1108476597
Category : Business & Economics
Languages : en
Pages : 297
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Book Description
A readable, digestible introduction to essential theory and wealth of applications, with a vast set of examples and numerous exercises.
Author: Bradley Efron
Publisher: Cambridge University Press
ISBN: 1108805434
Category : Mathematics
Languages : en
Pages : 264
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Book Description
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: Imre Csiszár
Publisher: Now Publishers Inc
ISBN: 9781933019055
Category : Computers
Languages : en
Pages : 128
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Book Description
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.
