Comparative statistical inference:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester [u.a.]
Wiley
1999
|
| Edition: | 3. ed. |
| Series: | Wiley series in probability and statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 381 S. graph. Darst. |
| ISBN: | 0471976431 |
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| adam_text | Titel: Comparative statistical inference
Autor: Barnett, Vic
Jahr: 1999
Comparative Statistical Inference
Third Edition
Vic Barnett
Professor of Environmental Statistics
University of Nottingham, UK
JOHN WILEY SONS, LTD
Chichester • New York • Weinheim • Brisbane • Singapore • Toronto
Contents
Preface
Preface to Second Edition
Preface to Third Edition
Acknowledgements
xi
xv
xvii
xix
Chapter 1. Introduction: Statistical Inference and
Decision-making 1
1.1 What is Statistics? 1
1.2 Probability Models 4
1.3 Relevant Information 7
1.4 Statistical Inference and Decision-making 13
1.5 Different Approaches 15
1.6 Arbitrariness and Controversy 19
1.7 Historical Comment and Further References 23
Chapter 2. An Illustration of the Different
Approaches 29
2.1 A Practical Example 29
2.2 Sample Data as the Sole Source of Information: the
Classical Approach 32
2.2.1 Batch Quality 33
2.2.2 Component Lifetimes 43
2.3 Relevant Prior Information: the Bayesian Approach 47
2.3.1 Prior Information on Batch Quality 47
2.3.2 Prior Attitudes about Component Lifetimes 53
2.4 Costs and Consequences: Simple Decision Theory
Ideas 54
2.5 Comment and Comparisons 62
Chapter 3. Probability 65
3.1 Types of Probability 65
3.2 Classical Probability 73
3.3 The Frequency View 76
3.4 Logical Probability 81
3.5 Subjective Probability 84
viii
CONTENTS
3.6 Other Viewpoints 92
3.6.1 Chaos 92
3.6.2 Fuzzy Set Theory 94
3.6.3 Risk, Uncertainty and Sensitivity Analysis 95
3.7 Some Historical Background 96
3.8 And So ... 97
3.9 And Yet... 98
Chapter 4. Utility and Decision-making 99
4.1 Setting a Value on Rewards and Consequences 101
4.2 The Rational Expression of Preferences 106
4.3 Preferences for Prospects and Mixtures of Prospects 108
4.4 The Numerical Assessment of Prospects 110
4.5 The Measurement of Utilities 111
4.5.1 Formal Construction of Utilities 111
4.5.2 Personal Expression of Utilities 113
4.6 Decision-making 115
4.7 The Utility of Money 116
4.8 Comment: Mathematical Refinements: Distinctions of
Attitüde 119
Chapter 5. Classical Inference 123
5.1 Basic Aims and Concepts 125
5.1.1 Information and its Representation 127
5.2 Estimation and Testing Hypotheses—the Dual Aims 131
5.3 Point Estimation 137
5.3.1 Criteria for Point Estimators 137
5.3.2 Optimum Estimators 144
5.3.3 Methods of Constructing Estimators 152
5.3.4 Estimating Several Parameters 162
5.4 Testing Statistical Hypotheses 165
5.4.1 Criteria for Hypothesis Tests 166
5.4.2 Uniformly Most Powerful Tests 171
5.4.3 Construction of Tests 177
5.5 Region and Interval Estimates 181
5.6 Ancillarity, Conditionality, Modified forms of
Sufficiency and Likelihood 185
5.6.1 The Sufficiency, Conditionality and
Likelihood Principles 186
5.6.2 Modified Likelihood Forms (Marginal,
Partial, Profile, etc.) 189
5.7 Comment and Controversy 191
5.7.1 Initial and Final Precision 192
5.7.2 Prediction and Tolerance Regions 194
5.7.3 Hypothesis Tests and Decisions 195
5.7.4 Counter Criticism 197
CONTENTS
Chapter 6. Bayesian Inference
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
Thomas Bayes
The Bayesian Method
Particular Techniques
Prediction in Bayesian Inference
Prior Information
6.5.1 Prior Ignorance
6.5.2 Vague Prior Knowledge
6.5.3 Substantial Prior Knowledge
6.5.4 Conjugate Prior Distributions
6.5.5 Quantifying Subjective Prior Information
Computing Posterior Distributions
Empirical Bayes methods: Meta-prior Distributions
6.7.1 Empirical Bayes Methods
6.7.2 Meta-prior Distributions
Comment and Controversy
6.8.1 Interpretation of Prior and Posterior
Distributions
6.8.2 Sufficiency, Likelihood and Unbiasedness
6.8.3 Controversy
Chapter 7. Decision Theory
7.1
7.2
7.3
7.4
7.5
7.6
An Illustrative Example
Basic Concepts and Principles
7.2.1 The Decision Theory Model
7.2.2 The No-data Situation
7.2.3 Sample Data
Attainment and Implementation
7.3.1 Admissibility and Unbiasedness
7.3.2 Determination of Bayes Decision Rules
7.3.3 Minimax Decision Rules
7.3.4 Estimation and Hypothesis Testing
Problems with Finite Numbers of Actions, and States
of Nature
7.4.1 The No-data Problem
7.4.2 The Use of Sample Data
Extensions and Modifications
Critical Comment
Chapter 8. Other Approaches
8.1 Fiducial Inference
8.2 Likelihood Inference
8.3 Plausibility Inference
8.4 Structural Inference
8.5 Pivotal Inference
8.6 Information
IX
201
201
, 203
207
217
219
220
225
228
230
234
235
238
238
240
242
242
245
247
251
253
262
264
264
265
269
270
275
278
279
286
286
287
289
292
297
298
306
311
313
319
322
CONTENTS
8.7 Causal Inference 325
8.8 Prequential Inference 326
8.9 Indeterminism and the Mathematics of Philosophy 327
Chapter 9. Perspective 331
References 337
Index 365
|
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| spelling | Barnett, Vic Verfasser aut Comparative statistical inference Vic Barnett 3. ed. Chichester [u.a.] Wiley 1999 XIV, 381 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Besliskunde gtt Prise de décision (Statistique) Statistique mathématique Statistische toetsen gtt Mathematical statistics Statistical decision Statistische Entscheidungstheorie (DE-588)4077850-2 gnd rswk-swf Inferenzstatistik (DE-588)4247120-5 gnd rswk-swf Statistische Schlussweise (DE-588)4182963-3 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Statistische Entscheidungstheorie (DE-588)4077850-2 s DE-604 Inferenzstatistik (DE-588)4247120-5 s Statistische Schlussweise (DE-588)4182963-3 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008568757&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Barnett, Vic Comparative statistical inference Besliskunde gtt Prise de décision (Statistique) Statistique mathématique Statistische toetsen gtt Mathematical statistics Statistical decision Statistische Entscheidungstheorie (DE-588)4077850-2 gnd Inferenzstatistik (DE-588)4247120-5 gnd Statistische Schlussweise (DE-588)4182963-3 gnd |
| subject_GND | (DE-588)4077850-2 (DE-588)4247120-5 (DE-588)4182963-3 (DE-588)4151278-9 |
| title | Comparative statistical inference |
| title_auth | Comparative statistical inference |
| title_exact_search | Comparative statistical inference |
| title_full | Comparative statistical inference Vic Barnett |
| title_fullStr | Comparative statistical inference Vic Barnett |
| title_full_unstemmed | Comparative statistical inference Vic Barnett |
| title_short | Comparative statistical inference |
| title_sort | comparative statistical inference |
| topic | Besliskunde gtt Prise de décision (Statistique) Statistique mathématique Statistische toetsen gtt Mathematical statistics Statistical decision Statistische Entscheidungstheorie (DE-588)4077850-2 gnd Inferenzstatistik (DE-588)4247120-5 gnd Statistische Schlussweise (DE-588)4182963-3 gnd |
| topic_facet | Besliskunde Prise de décision (Statistique) Statistique mathématique Statistische toetsen Mathematical statistics Statistical decision Statistische Entscheidungstheorie Inferenzstatistik Statistische Schlussweise Einführung |
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