Exponential Families and Conditioning PDF Download

Author: Ole E. Barndorff-Nielsen
Publisher:
ISBN:
Category : Distribution (Probability theory)
Languages : en
Pages : 268

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Book Description

Author: Lawrence D. Brown
Publisher: IMS
ISBN: 9780940600102
Category : Business & Economics
Languages : en
Pages : 302

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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: 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: Wilfrid S. Kendall
Publisher: Routledge
ISBN: 1351413724
Category : Mathematics
Languages : en
Pages : 419

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Book Description
Stochastic geometry involves the study of random geometric structures, and blends geometric, probabilistic, and statistical methods to provide powerful techniques for modeling and analysis. Recent developments in computational statistical analysis, particularly Markov chain Monte Carlo, have enormously extended the range of feasible applications. Stochastic Geometry: Likelihood and Computation provides a coordinated collection of chapters on important aspects of the rapidly developing field of stochastic geometry, including: o a "crash-course" introduction to key stochastic geometry themes o considerations of geometric sampling bias issues o tesselations o shape o random sets o image analysis o spectacular advances in likelihood-based inference now available to stochastic geometry through the techniques of Markov chain Monte Carlo

Author: Uwe Küchler
Publisher: Springer Science & Business Media
ISBN: 0387227652
Category : Mathematics
Languages : en
Pages : 325

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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: 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: Ronald W. Butler
Publisher: Cambridge University Press
ISBN: 1139466518
Category : Mathematics
Languages : en
Pages : 548

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Book Description
Modern statistical methods use complex, sophisticated models that can lead to intractable computations. Saddlepoint approximations can be the answer. Written from the user's point of view, this book explains in clear language how such approximate probability computations are made, taking readers from the very beginnings to current applications. The core material is presented in chapters 1-6 at an elementary mathematical level. Chapters 7-9 then give a highly readable account of higher-order asymptotic inference. Later chapters address areas where saddlepoint methods have had substantial impact: multivariate testing, stochastic systems and applied probability, bootstrap implementation in the transform domain, and Bayesian computation and inference. No previous background in the area is required. Data examples from real applications demonstrate the practical value of the methods. Ideal for graduate students and researchers in statistics, biostatistics, electrical engineering, econometrics, and applied mathematics, this is both an entry-level text and a valuable reference.

Author: Frank Nielsen
Publisher: Springer Nature
ISBN: 3030654591
Category : Science
Languages : en
Pages : 274

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Book Description
This book focuses on information-geometric manifolds of structured data and models and related applied mathematics. It features new and fruitful interactions between several branches of science: Advanced Signal/Image/Video Processing, Complex Data Modeling and Analysis, Statistics on Manifolds, Topology/Machine/Deep Learning and Artificial Intelligence. The selection of applications makes the book a substantial information source, not only for academic scientist but it is also highly relevant for industry. The book project was initiated following discussions at the international conference GSI’2019 – Geometric Science of Information that was held at ENAC, Toulouse (France).