UID:
almafu_9960117371602883
Umfang:
1 online resource (xx, 500 pages) :
,
digital, PDF file(s).
Ausgabe:
First edition.
ISBN:
1-316-44332-9
,
1-316-44677-8
,
1-139-04667-5
Serie:
Cambridge series in statistical and probabilistic mathematics ; 41
Inhalt:
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.
Anmerkung:
Title from publisher's bibliographic system (viewed on 08 Mar 2016).
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Cover -- Half-title page -- Series information -- Title page -- Copyright information -- Dedication -- Table of contents -- Preface -- 1 Confidence, likelihood, probability: An invitation -- 1.1 Introduction -- 1.2 Probability -- 1.3 Inverse probability -- 1.4 Likelihood -- 1.5 Frequentism -- 1.6 Confidence and confidence curves -- 1.7 Fiducial probability and confidence -- 1.8 Why not go Bayesian? -- 1.9 Notes on the literature -- 2 Inference in parametric models -- 2.1 Introduction -- 2.2 Likelihood methods and first-order large-sample theory -- 2.3 Sufficiency and the likelihood principle -- 2.4 Focus parameters, pivots and profile likelihoods -- 2.5 Bayesian inference -- 2.6 Related themes and issues -- 2.7 Notes on the literature -- Exercises -- 3 Confidence distributions -- 3.1 Introduction -- 3.2 Confidence distributions and statistical inference -- 3.3 Graphical focus summaries -- 3.4 General likelihood-based recipes -- 3.5 Confidence distributions for the linear regression model -- 3.6 Contingency tables -- 3.7 Testing hypotheses via confidence for alternatives -- 3.8 Confidence for discrete parameters -- 3.9 Notes on the literature -- Exercises -- 4 Further developments for confidence distribution -- 4.1 Introduction -- 4.2 Bounded parameters and bounded confidence -- 4.3 Random and mixed effects models -- 4.4 The Neyman-Scott problem -- 4.5 Multimodality -- 4.6 Ratio of two normal means -- 4.7 Hazard rate models -- 4.8 Confidence inference for Markov chains -- 4.9 Time series and models with dependence -- 4.10 Bivariate distributions and the average confidence density -- 4.11 Deviance intervals versus minimum length intervals -- 4.12 Notes on the literature -- Exercises -- 5 Invariance, sufficiency and optimality for confidence distributions -- 5.1 Confidence power -- 5.2 Invariance for confidence distributions.
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5.3 Loss and risk functions for confidence distributions -- 5.4 Sufficiency and risk for confidence distributions -- 5.5 Uniformly optimal confidence for exponential families -- 5.6 Optimality of component confidence distributions -- 5.7 Notes on the literature -- Exercises -- 6 The fiducial argument -- 6.1 The initial argument -- 6.2 The controversy -- 6.3 Paradoxes -- 6.4 Fiducial distributions and Bayesian posteriors -- 6.5 Coherence by restricting the range: Invariance or irrelevance? -- 6.6 Generalised fiducial inference -- 6.7 Further remarks -- 6.8 Notes on the literature -- Exercises -- 7 Improved approximations for confidence distributions -- 7.1 Introduction -- 7.2 From first-order to second-order approximations -- 7.3 Pivot tuning -- 7.4 Bartlett corrections for the deviance -- 7.5 Median-bias correction -- 7.6 The t-bootstrap and abc-bootstrap method -- 7.7 Saddlepoint approximations and the magic formula -- 7.8 Approximations to the gold standard in two test cases -- 7.9 Further remarks -- 7.10 Notes on the literature -- Exercises -- 8 Exponential families and generalised linear models -- 8.1 The exponential family -- 8.2 Applications -- 8.3 A bivariate Poisson model -- 8.4 Generalised linear models -- 8.5 Gamma regression models -- 8.6 Flexible exponential and generalised linear models -- 8.7 Strauss, Ising, Potts, Gibbs -- 8.8 Generalised linear-linear models -- 8.9 Notes on the literature -- Exercises -- 9 Confidence distributions in higher dimensions -- 9.1 Introduction -- 9.2 Normally distributed data -- 9.3 Confidence curves from deviance functions -- 9.4 Potential bias and the marginalisation paradox -- 9.5 Product confidence curves -- 9.6 Confidence bands for curves -- 9.7 Dependencies between confidence curves -- 9.8 Notes on the literature -- Exercises -- 10 Likelihoods and confidence likelihoods -- 10.1 Introduction.
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10.2 The normal conversion -- 10.3 Exact conversion -- 10.4 Likelihoods from prior distributions -- 10.5 Likelihoods from confidence intervals -- 10.6 Discussion -- 10.7 Notes on the literature -- Exercises -- 11 Confidence in non- and semiparametric models -- 11.1 Introduction -- 11.2 Confidence distributions for distribution functions -- 11.3 Confidence distributions for quantiles -- 11.4 Wilcoxon for location -- 11.5 Empirical likelihood -- 11.6 Notes on the literature -- Exercises -- 12 Predictions and confidence -- 12.1 Introduction -- 12.2 The next data point -- 12.3 Comparison with Bayesian prediction -- 12.4 Prediction in regression models -- 12.5 Time series and kriging -- 12.6 Spatial regression and prediction -- 12.7 Notes on the literature -- Exercises -- 13 Meta-analysis and combination of information -- 13.1 Introduction -- 13.2 Aspects of scientific reporting -- 13.3 Confidence distributions in basic meta-analysis -- 13.4 Meta-analysis for an ensemble of parameter estimates -- 13.5 Binomial count data -- 13.6 Direct combination of confidence distributions -- 13.7 Combining confidence likelihoods -- 13.8 Notes on the literature -- Exercises -- 14 Applications -- 14.1 Introduction -- 14.2 Golf putting -- 14.3 Bowheads -- 14.4 Sims and economic prewar development in the United States -- 14.5 Olympic unfairness -- 14.6 Norwegian income -- 14.7 Meta-analysis of two-by-two tables from clinical trials -- 14.8 Publish (and get cited) or perish -- 14.9 Notes on the literature -- Exercises -- 15 Finale: Summary, and a look into the future -- 15.1 A brief summary of the book -- 15.2 Theories of epistemic probability and evidential reasoning -- 15.3 Why the world need not be Bayesian after all -- 15.4 Unresolved issues -- 15.5 Finale -- Overview of examples and data -- Appendix: Large-sample theory with applications.
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A.1 Convergence in probability -- A.2 Convergence in distribution -- A.3 Central limit theorems and the delta method -- A.4 Minimisers of random convex functions -- A.5 Likelihood inference outside model conditions -- A.6 Robust parametric inference -- A.7 Model selection -- A.8 Notes on the literature -- References -- Name Index -- Subject Index.
,
English
Weitere Ausg.:
ISBN 0-521-86160-8
Sprache:
Englisch
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