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Confidence, Likelihood, Probability: Statistical Inference with Confidence Distributions [Hardback]

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(Universitetet i Oslo), (Universitetet i Oslo)
  • Formāts: Hardback, 511 pages, height x width x depth: 260x184x31 mm, weight: 1090 g, Worked examples or Exercises; 17 Tables, unspecified; 147 Line drawings, unspecified
  • Sērija : Cambridge Series in Statistical and Probabilistic Mathematics
  • Izdošanas datums: 24-Feb-2016
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 0521861608
  • ISBN-13: 9780521861601
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Confidence, Likelihood, Probability: Statistical Inference with Confidence DistributionsPalielināt
  • Formāts: Hardback, 511 pages, height x width x depth: 260x184x31 mm, weight: 1090 g, Worked examples or Exercises; 17 Tables, unspecified; 147 Line drawings, unspecified
  • Sērija : Cambridge Series in Statistical and Probabilistic Mathematics
  • Izdošanas datums: 24-Feb-2016
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 0521861608
  • ISBN-13: 9780521861601
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780521861601.html
Keywords:
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 con dence from different sources of information, and they can make complex models amenable to objective and indeed prior-free analysis for less subjectively inclined statisticians. Fisher's concept of fiducial probability plays an important role.

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 con dence 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.

Recenzijas

'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

Papildus informācija

This is the first book to develop a methodology of confidence distributions, with a lively mix of theory, illustrations, applications and exercises.
Preface xiii
1 Confidence, likelihood, probability: An invitation 1(22)
1.1 Introduction
1(3)
1.2 Probability
4(2)
1.3 Inverse probability
6(1)
1.4 Likelihood
7(1)
1.5 Frequentism
8(2)
1.6 Confidence and confidence curves
10(4)
1.7 Fiducial probability and confidence
14(2)
1.8 Why not go Bayesian?
16(3)
1.9 Notes on the literature
19(4)
2 Inference in parametric models 23(32)
2.1 Introduction
23(1)
2.2 Likelihood methods and first-order large-sample theory
24(6)
2.3 Sufficiency and the likelihood principle
30(2)
2.4 Focus parameters, pivots and profile likelihoods
32(8)
2.5 Bayesian inference
40(2)
2.6 Related themes and issues
42(6)
2.7 Notes on the literature
48(2)
Exercises
50(5)
3 Confidence distributions 55(45)
3.1 Introduction
55(1)
3.2 Confidence distributions and statistical inference
56(9)
3.3 Graphical focus summaries
65(4)
3.4 General likelihood-based recipes
69(3)
3.5 Confidence distributions for the linear regression model
72(6)
3.6 Contingency tables
78(2)
3.7 Testing hypotheses via confidence for alternatives
80(3)
3.8 Confidence for discrete parameters
83(8)
3.9 Notes on the literature
91(1)
Exercises
92(8)
4 Further developments for confidence distribution 100(54)
4.1 Introduction
100(1)
4.2 Bounded parameters and bounded confidence
100(7)
4.3 Random and mixed effects models
107(4)
4.4 The Neyman—Scott problem
111(4)
4.5 Multimodality
115(2)
4.6 Ratio of two normal means
117(5)
4.7 Hazard rate models
122(6)
4.8 Confidence inference for Markov chains
128(5)
4.9 Time series and models with dependence
133(5)
4.10 Bivariate distributions and the average confidence density
138(2)
4.11 Deviance intervals versus minimum length intervals
140(2)
4.12 Notes on the literature
142(2)
Exercises
144(10)
5 Invariance, sufficiency and optimality for confidence distributions 154(31)
5.1 Confidence power
154(3)
5.2 Invariance for confidence distributions
157(4)
5.3 Loss and risk functions for confidence distributions
161(4)
5.4 Sufficiency and risk for confidence distributions
165(8)
5.5 Uniformly optimal confidence for exponential families
173(4)
5.6 Optimality of component confidence distributions
177(2)
5.7 Notes on the literature
179(1)
Exercises
180(5)
6 The fiducial argument 185(19)
6.1 The initial argument
185(3)
6.2 The controversy
188(3)
6.3 Paradoxes
191(2)
6.4 Fiducial distributions and Bayesian posteriors
193(1)
6.5 Coherence by restricting the range: Invariance or irrelevance?
194(3)
6.6 Generalised fiducial inference
197(3)
6.7 Further remarks
200(1)
6.8 Notes on the literature
201(1)
Exercises
202(2)
7 Improved approximations for confidence distributions 204(29)
7.1 Introduction
204(1)
7.2 From first-order to second-order approximations
205(3)
7.3 Pivot tuning
208(2)
7.4 Bartlett corrections for the deviance
210(4)
7.5 Median-bias correction
214(3)
7.6 The t-bootstrap and abc-bootstrap method
217(2)
7.7 Saddlepoint approximations and the magic formula
219(3)
7.8 Approximations to the gold standard in two test cases
222(5)
7.9 Further remarks
227(1)
7.10 Notes on the literature
228(1)
Exercises
229(4)
8 Exponential families and generalised linear models 233(41)
8.1 The exponential family
233(2)
8.2 Applications
235(6)
8.3 A bivariate Poisson model
241(5)
8.4 Generalised linear models
246(3)
8.5 Gamma regression models
249(3)
8.6 Flexible exponential and generalised linear models
252(4)
8.7 Strauss, Ising, Potts, Gibbs
256(4)
8.8 Generalised linear-linear models
260(4)
8.9 Notes on the literature
264(2)
Exercises
266(8)
9 Confidence distributions in higher dimensions 274(21)
9.1 Introduction
274(1)
9.2 Normally distributed data
275(3)
9.3 Confidence curves from deviance functions
278(1)
9.4 Potential bias and the marginalisation paradox
279(1)
9.5 Product confidence curves
280(4)
9.6 Confidence bands for curves
284(7)
9.7 Dependencies between confidence curves
291(1)
9.8 Notes on the literature
292(1)
Exercises
292(3)
10 Likelihoods and confidence likelihoods 295(22)
10.1 Introduction
295(3)
10.2 The normal conversion
298(3)
10.3 Exact conversion
301(1)
10.4 Likelihoods from prior distributions
302(3)
10.5 Likelihoods from confidence intervals
305(6)
10.6 Discussion
311(1)
10.7 Notes on the literature
312(1)
Exercises
313(4)
11 Confidence in non- and semiparametric models 317(19)
11.1 Introduction
317(1)
11.2 Confidence distributions for distribution functions
318(1)
11.3 Confidence distributions for quantiles
318(6)
11.4 Wilcoxon for location
324(1)
11.5 Empirical likelihood
325(7)
11.6 Notes on the literature
332(1)
Exercises
333(3)
12 Predictions and confidence 336(24)
12.1 Introduction
336(1)
12.2 The next data point
337(6)
12.3 Comparison with Bayesian prediction
343(3)
12.4 Prediction in regression models
346(4)
12.5 Time series and kriging
350(3)
12.6 Spatial regression and prediction
353(3)
12.7 Notes on the literature
356(1)
Exercises
356(4)
13 Meta-analysis and combination of information 360(23)
13.1 Introduction
360(3)
13.2 Aspects of scientific reporting
363(1)
13.3 Confidence distributions in basic meta-analysis
364(7)
13.4 Meta-analysis for an ensemble of parameter estimates
371(3)
13.5 Binomial count data
374(1)
13.6 Direct combination of confidence distributions
375(1)
13.7 Combining confidence likelihoods
376(3)
13.8 Notes on the literature
379(1)
Exercises
380(3)
14 Applications 383(35)
14.1 Introduction
383(1)
14.2 Golf putting
384(3)
14.3 Bowheads
387(2)
14.4 Sims and economic prewar development in the United States
389(2)
14.5 Olympic unfairness
391(5)
14.6 Norwegian income
396(5)
14.7 Meta-analysis of two-by-two tables from clinical trials
401(8)
14.8 Publish (and get cited) or perish
409(3)
14.9 Notes on the literature
412(1)
Exercises
413(5)
15 Finale: Summary, and a look into the future 418(19)
15.1 A brief summary of the book
418(5)
15.2 Theories of epistemic probability and evidential reasoning
423(5)
15.3 Why the world need not be Bayesian after all
428(2)
15.4 Unresolved issues
430(5)
15.5 Finale
435(2)
Overview of examples and data 437(10)
Appendix. Large-sample theory with applications 447(24)
A.1 Convergence in probability
447(1)
A.2 Convergence in distribution
448(1)
A.3 Central limit theorems and the delta method
449(3)
A.4 Minimisers of random convex functions
452(2)
A.5 Likelihood inference outside model conditions
454(4)
A.6 Robust parametric inference
458(4)
A.7 Model selection
462(2)
A.8 Notes on the literature
464(1)
Exercises
464(7)
References 471(18)
Name index 489(6)
Subject index 495
Tore Schweder is a Professor of Statistics in the Department of Economics and at the Centre for Ecology and Evolutionary Synthesis at the University of Oslo. Nils Lid Hjort is Professor of Mathematical Statistics in the Department of Mathematics at the University of Oslo.