Confidence, Likelihood, Probability

Confidence, Likelihood, Probability
Title Confidence, Likelihood, Probability PDF eBook
Author Tore Schweder
Publisher Cambridge University Press
Pages 521
Release 2016-02-24
Genre Mathematics
ISBN 1316445054

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This lively book lays out a methodology of confidence distributions and puts them through their paces. Among other merits, they lead to optimal combinations of confidence from different sources of information, and they can make complex models amenable to objective and indeed prior-free analysis for less subjectively inclined statisticians. The generous mixture of theory, illustrations, applications and exercises is suitable for statisticians at all levels of experience, as well as for data-oriented scientists. Some confidence distributions are less dispersed than their competitors. This concept leads to a theory of risk functions and comparisons for distributions of confidence. Neyman–Pearson type theorems leading to optimal confidence are developed and richly illustrated. Exact and optimal confidence distribution is the gold standard for inferred epistemic distributions. Confidence distributions and likelihood functions are intertwined, allowing prior distributions to be made part of the likelihood. Meta-analysis in likelihood terms is developed and taken beyond traditional methods, suiting it in particular to combining information across diverse data sources.

Confidence, Likelihood, Probability

Confidence, Likelihood, Probability
Title Confidence, Likelihood, Probability PDF eBook
Author Tore Schweder
Publisher Cambridge University Press
Pages 521
Release 2016-02-24
Genre Business & Economics
ISBN 0521861608

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This is the first book to develop a methodology of confidence distributions, with a lively mix of theory, illustrations, applications and exercises.

Empirical Likelihood

Empirical Likelihood
Title Empirical Likelihood PDF eBook
Author Art B. Owen
Publisher CRC Press
Pages 322
Release 2001-05-18
Genre Mathematics
ISBN 1420036157

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Empirical likelihood provides inferences whose validity does not depend on specifying a parametric model for the data. Because it uses a likelihood, the method has certain inherent advantages over resampling methods: it uses the data to determine the shape of the confidence regions, and it makes it easy to combined data from multiple sources. It al

The Likelihood Principle

The Likelihood Principle
Title The Likelihood Principle PDF eBook
Author James O. Berger
Publisher IMS
Pages 266
Release 1988
Genre Mathematics
ISBN 9780940600133

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Confidence Intervals in Generalized Regression Models

Confidence Intervals in Generalized Regression Models
Title Confidence Intervals in Generalized Regression Models PDF eBook
Author Esa Uusipaikka
Publisher CRC Press
Pages 328
Release 2008-07-25
Genre Mathematics
ISBN 1420060384

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A Cohesive Approach to Regression Models Confidence Intervals in Generalized Regression Models introduces a unified representation-the generalized regression model (GRM)-of various types of regression models. It also uses a likelihood-based approach for performing statistical inference from statistical evidence consisting of data a

Statistical Evidence

Statistical Evidence
Title Statistical Evidence PDF eBook
Author Richard Royall
Publisher Routledge
Pages 212
Release 2017-11-22
Genre Mathematics
ISBN 1351414550

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Interpreting statistical data as evidence, Statistical Evidence: A Likelihood Paradigm focuses on the law of likelihood, fundamental to solving many of the problems associated with interpreting data in this way. Statistics has long neglected this principle, resulting in a seriously defective methodology. This book redresses the balance, explaining why science has clung to a defective methodology despite its well-known defects. After examining the strengths and weaknesses of the work of Neyman and Pearson and the Fisher paradigm, the author proposes an alternative paradigm which provides, in the law of likelihood, the explicit concept of evidence missing from the other paradigms. At the same time, this new paradigm retains the elements of objective measurement and control of the frequency of misleading results, features which made the old paradigms so important to science. The likelihood paradigm leads to statistical methods that have a compelling rationale and an elegant simplicity, no longer forcing the reader to choose between frequentist and Bayesian statistics.

Statistical Inference Based on the likelihood

Statistical Inference Based on the likelihood
Title Statistical Inference Based on the likelihood PDF eBook
Author Adelchi Azzalini
Publisher Routledge
Pages 356
Release 2017-11-13
Genre Mathematics
ISBN 1351414461

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The Likelihood plays a key role in both introducing general notions of statistical theory, and in developing specific methods. This book introduces likelihood-based statistical theory and related methods from a classical viewpoint, and demonstrates how the main body of currently used statistical techniques can be generated from a few key concepts, in particular the likelihood. Focusing on those methods, which have both a solid theoretical background and practical relevance, the author gives formal justification of the methods used and provides numerical examples with real data.