Fundamentals of Statistical Exponential Families

Fundamentals of Statistical Exponential Families

Author: Lawrence D. Brown

Publisher:

Published: 2008*

Total Pages: 284

ISBN-13:

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This e-book is the product of Project Euclid and its mission to advance scholarly communication in the field of theoretical and applied mathematics and statistics. Project Euclid was developed and deployed by the Cornell University Library and is jointly managed by Cornell and the Duke University Press.


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.


Foundations of Statistical Inference

Foundations of Statistical Inference

Author: Yoel Haitovsky

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 227

ISBN-13: 3642574106

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This volume is a collection of papers presented at a conference held in Shoresh Holiday Resort near Jerusalem, Israel, in December 2000 organized by the Israeli Ministry of Science, Culture and Sport. The theme of the conference was "Foundation of Statistical Inference: Applications in the Medical and Social Sciences and in Industry and the Interface of Computer Sciences". The following is a quotation from the Program and Abstract booklet of the conference. "Over the past several decades, the field of statistics has seen tremendous growth and development in theory and methodology. At the same time, the advent of computers has facilitated the use of modern statistics in all branches of science, making statistics even more interdisciplinary than in the past; statistics, thus, has become strongly rooted in all empirical research in the medical, social, and engineering sciences. The abundance of computer programs and the variety of methods available to users brought to light the critical issues of choosing models and, given a data set, the methods most suitable for its analysis. Mathematical statisticians have devoted a great deal of effort to studying the appropriateness of models for various types of data, and defining the conditions under which a particular method work. " In 1985 an international conference with a similar title* was held in Is rael. It provided a platform for a formal debate between the two main schools of thought in Statistics, the Bayesian, and the Frequentists.


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 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 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.


Computational Information Geometry

Computational Information Geometry

Author: Frank Nielsen

Publisher: Springer

Published: 2016-11-24

Total Pages: 312

ISBN-13: 3319470582

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This book focuses on the application and development of information geometric methods in the analysis, classification and retrieval of images and signals. It provides introductory chapters to help those new to information geometry and applies the theory to several applications. This area has developed rapidly over recent years, propelled by the major theoretical developments in information geometry, efficient data and image acquisition and the desire to process and interpret large databases of digital information. The book addresses both the transfer of methodology to practitioners involved in database analysis and in its efficient computational implementation.