Exponential Families In Theory And Practice

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Exponential Families In Theory And Practice

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Author : Bradley Efron
language : en
Publisher: Cambridge University Press
Release Date : 2022-12-15

Exponential Families In Theory And Practice written by Bradley Efron and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-15 with Mathematics categories.

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.

Information And Exponential Families

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Author : O. Barndorff-Nielsen
language : en
Publisher: John Wiley & Sons
Release Date : 2014-05-07

Information And Exponential Families written by O. Barndorff-Nielsen and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-07 with Mathematics categories.

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.

Fundamentals Of Statistical Exponential Families

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Author : Lawrence D. Brown
language : en
Publisher: IMS
Release Date : 1986

Fundamentals Of Statistical Exponential Families written by Lawrence D. Brown and has been published by IMS this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Business & Economics categories.

Computer Age Statistical Inference Student Edition

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Author : Bradley Efron
language : en
Publisher: Cambridge University Press
Release Date : 2021-06-17

Computer Age Statistical Inference Student Edition written by Bradley Efron and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-17 with Computers categories.

Now in paperback and fortified with exercises, this brilliant, enjoyable text demystifies data science, statistics and machine learning.

Multivariate Exponential Families A Concise Guide To Statistical Inference

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Author : Stefan Bedbur
language : en
Publisher: Springer Nature
Release Date : 2021-10-07

Multivariate Exponential Families A Concise Guide To Statistical Inference written by Stefan Bedbur and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-07 with Mathematics categories.

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 Family Nonlinear Models

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Author : Bo-Cheng Wei
language : en
Publisher:
Release Date : 1998-09

Exponential Family Nonlinear Models written by Bo-Cheng Wei and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-09 with Mathematics categories.

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.

Large Scale Inference

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Author : Bradley Efron
language : en
Publisher: Cambridge University Press
Release Date : 2012-11-29

Large Scale Inference written by Bradley Efron and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-29 with Mathematics categories.

We live in a new age for statistical inference, where modern scientific technology such as microarrays and fMRI machines routinely produce thousands and sometimes millions of parallel data sets, each with its own estimation or testing problem. Doing thousands of problems at once is more than repeated application of classical methods. Taking an empirical Bayes approach, Bradley Efron, inventor of the bootstrap, shows how information accrues across problems in a way that combines Bayesian and frequentist ideas. Estimation, testing and prediction blend in this framework, producing opportunities for new methodologies of increased power. New difficulties also arise, easily leading to flawed inferences. This book takes a careful look at both the promise and pitfalls of large-scale statistical inference, with particular attention to false discovery rates, the most successful of the new statistical techniques. Emphasis is on the inferential ideas underlying technical developments, illustrated using a large number of real examples.

International Encyclopedia Of Statistical Science

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Author : Miodrag Lovric
language : en
Publisher: Springer Nature
Release Date : 2025-06-19

International Encyclopedia Of Statistical Science written by Miodrag Lovric and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-19 with Mathematics categories.

The International Encyclopedia of Statistical Science stands as a monumental effort to enrich statistics education globally, particularly in regions facing educational challenges. By amalgamating the expertise of over 700 authors from 110 countries, including Nobel Laureates and presidents of statistical societies, it offers an unparalleled resource for readers worldwide. This encyclopedia is not just a collection of entries; it is a concerted effort to revive statistics as a vibrant, critical field of study and application. Providing a comprehensive and accessible account of statistical terms, methods, and applications, it enables readers to gain a quick insight into the subject, regardless of their background. This work serves to refresh and expand the knowledge of researchers, managers, and practitioners, highlighting the relevance and applicability of statistics across various fields, from economics and business to healthcare and public policy. Furthermore, it aims to inspire students by demonstrating the significance of statistics in solving real-world problems, thus encouraging a new generation to explore and contribute to the field.

Graphical Models Exponential Families And Variational Inference

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Author : Martin J. Wainwright
language : en
Publisher: Now Publishers Inc
Release Date : 2008

Graphical Models Exponential Families And Variational Inference written by Martin J. Wainwright and has been published by Now Publishers Inc this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Computers categories.

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.

Principles Of Statistical Inference

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Author : D. R. Cox
language : en
Publisher: Cambridge University Press
Release Date : 2006-08-10

Principles Of Statistical Inference written by D. R. Cox and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-10 with Mathematics categories.

In this definitive book, D. R. Cox gives a comprehensive and balanced appraisal of statistical inference. He develops the key concepts, describing and comparing the main ideas and controversies over foundational issues that have been keenly argued for more than two-hundred years. Continuing a sixty-year career of major contributions to statistical thought, no one is better placed to give this much-needed account of the field. An appendix gives a more personal assessment of the merits of different ideas. The content ranges from the traditional to the contemporary. While specific applications are not treated, the book is strongly motivated by applications across the sciences and associated technologies. The mathematics is kept as elementary as feasible, though previous knowledge of statistics is assumed. The book will be valued by every user or student of statistics who is serious about understanding the uncertainty inherent in conclusions from statistical analyses.