Confidence, Likelihood, Probability: Statistical Inference with Confidence Distr

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Confidence, Likelihood, Probability by Tore Schweder, Nils Lid Hjort

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

FORMAT
Hardcover LANGUAGE
English CONDITION
Brand New Publisher Description

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.

Table of Contents

1. Confidence, likelihood, probability: an invitation; 2. Interference in parametric models; 3. Confidence distributions; 4. Further developments for confidence distribution; 5. Invariance, sufficiency and optimality for confidence distributions; 6. The fiducial argument; 7. Improved approximations for confidence distributions; 8. Exponential families and generalised linear models; 9. Confidence distributions in higher dimensions; 10. Likelihoods and confidence likelihoods; 11. Confidence in non- and semiparametric models; 12. Predictions and confidence; 13. Meta-analysis and combination of information; 14. Applications; 15. Finale: summary, and a look into the future.

Review

'This book presents a detailed and wide-ranging account of an approach to inference that moves the discipline towards increased cohesion, avoiding the artificial distinction between testing and estimation. Innovative and thorough, it is sure to have an impact both in the foundations of inference and in a wide range of practical applications of inference.' Nancy Reid, University Professor of Statistical Sciences, University of Toronto
'I recommend this book very enthusiastically to any researcher interested in learning more about advanced likelihood theory, based on concepts like confidence distributions and fiducial distributions, and their links with other areas. The book explains in a very didactical way the concepts, their use, their interpretation, etc., illustrated by an impressive number of examples and data sets from a wide range of areas in statistics.' Ingrid Van Keilegom, Université Catholique de Louvain

Promotional

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

Review Quote

Advance praise: 'This book presents a detailed and wide-ranging account of an approach to inference that moves the discipline towards increased cohesion, avoiding the artificial distinction between testing and estimation. Innovative and thorough, it is sure to have an impact both in the foundations of inference and in a wide range of practical applications of inference.' Nancy Reid, University Professor of Statistical Sciences, University of Toronto

Promotional \"Headline\"

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

Description for Bookstore

The baby without the bathwater? This lively book lays out a methodology of confidence distributions and puts them through their paces with a generous mixture of theory, illustrations, applications and exercises - suitable for statisticians at all levels of experience, as well as for data-oriented scientists. The methodology yields posterior distributions for parameters, but without the Bayesian ingredients.

Description for Library

The baby without the bathwater? This lively book lays out a methodology of confidence distributions and puts them through their paces with a generous mixture of theory, illustrations, applications and exercises - suitable for statisticians at all levels of experience, as well as for data-oriented scientists. The methodology yields posterior distributions for parameters, but without the Bayesian ingredients.

Details ISBN0521861608 Author Nils Lid Hjort Publisher Cambridge University Press ISBN-10 0521861608 ISBN-13 9780521861601 Format Hardcover Imprint Cambridge University Press Subtitle Statistical Inference with Confidence Distributions Place of Publication Cambridge Country of Publication United Kingdom DEWEY 519.54 Language English Media Book Series Number 41 Short Title CONFIDENCE LIKELIHOOD PROBABIL Year 2016 Pages 511 Publication Date 2016-02-24 Affiliation Universitetet i Oslo UK Release Date 2016-02-24 AU Release Date 2016-02-24 NZ Release Date 2016-02-24 Series Cambridge Series in Statistical and Probabilistic Mathematics Alternative 9781139046671 Illustrations Worked examples or Exercises; 17 Tables, unspecified; 147 Line drawings, unspecified Audience Postgraduate, Research & Scholarly Country of Origin US Product Class Description Mathematics
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