Multivariate Exponential Families: A Concise Guide to Statistical Inference
Multivariate Exponential Families: A Concise Guide to Statistical Inference

Author: Stefan Bedbur

Publisher: Springer Nature

Published: 2021-10-07

Total Pages: 147

ISBN-13: 3030819000

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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.

Exponential Families of Stochastic Processes
Exponential Families of Stochastic Processes

Author: Uwe Küchler

Publisher: Springer Science & Business Media

Published: 2006-05-09

Total Pages: 325

ISBN-13: 0387227652

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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.

Statistical Modelling by Exponential Families
Statistical Modelling by Exponential Families

Author: Rolf Sundberg

Publisher: Cambridge University Press

Published: 2019-08-29

Total Pages: 297

ISBN-13: 1108476597

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

Information and Exponential Families
Information and Exponential Families

Author: O. Barndorff-Nielsen

Publisher: John Wiley & Sons

Published: 2014-05-07

Total Pages: 248

ISBN-13: 1118857372

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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.

Exponential Families in Theory and Practice
Exponential Families in Theory and Practice

Author: Bradley Efron

Publisher: Cambridge University Press

Published: 2022-12-15

Total Pages: 263

ISBN-13: 1108488900

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This accessible course on a central player in modern statistical practice connects models with methodology, without need for advanced math.

Exponential Family Nonlinear Models
Exponential Family Nonlinear Models

Author: Bo-Cheng Wei

Publisher:

Published: 1998-09

Total Pages: 248

ISBN-13:

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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.

Saddlepoint Approximations with Applications
Saddlepoint Approximations with Applications

Author: Ronald W. Butler

Publisher: Cambridge University Press

Published: 2007-08-16

Total Pages: 548

ISBN-13: 1139466518

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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.

Statistical Modelling by Exponential Families
Statistical Modelling by Exponential Families

Author: Rolf Sundberg

Publisher: Cambridge University Press

Published: 2019-08-29

Total Pages: 297

ISBN-13: 1108759912

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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 practical potential by connecting it with developments in areas like item response analysis, social network models, conditional independence and latent variable structures, and point process models. Extensions to incomplete data models and generalized linear models are also included. In addition, the author gives a concise account of the philosophy of Per Martin-Löf in order to connect statistical modelling with ideas in statistical physics, including Boltzmann's law. Written for graduate students and researchers with a background in basic statistical inference, the book includes a vast set of examples demonstrating models for applications and exercises embedded within the text as well as at the ends of chapters.