عنوان

Confidence, likelihood, probability :

0521861608

9780521861601

9781316446775 (PDF ebook)

Confidence, likelihood, probability :

[Book]

statistical inference with confidence distributions /

Tore Schweder, University of Oslo, Nils Lid Hjort, University of Oslo.

New York, NY :

Cambridge University Press,

2016.

xx, 500 pages :

illustrations ;

27 cm.

Cambridge series in statistical and probabilistic mathematics

Includes bibliographical references (pages 471-488) and indexes.

Machine generated contents note: 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 -- 2.1.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 -- 3.1.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 -- 4.1.Introduction

Note continued: 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 -- 5.1.Confidence power -- 5.2.Invariance for confidence distributions -- 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 -- 6.1.The initial argument -- 6.2.The controversy -- 6.3.Paradoxes -- 6.4.Fiducial distributions and Bayesian posteriors

Note continued: 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 -- 7.1.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 -- 8.1.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 -- 9.1.Introduction -- 9.2.Normally distributed data

Note continued: 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 -- 10.1.Introduction -- 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 -- 11.1.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 -- 12.1.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

Note continued: 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 -- Exercises.

Note continued: Exercises -- 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 -- 14.1.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 -- 15.1.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 -- A.1.Convergence in probability -- A.2.Convergence in distribution

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This 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.

9781316446775

Mathematical statistics.

Observed confidence levels (Statistics)

Probabilities.

Mathematical statistics.

Observed confidence levels (Statistics)

Probabilities.

Schweder, Tore.

Hjort, Nils Lid.

20200822120414.0

rda

[Book]

Y