Comparative statistical inference:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester [u.a.]
Wiley
1982
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| Ausgabe: | 2. ed. |
| Schriftenreihe: | Wiley series in probability and mathematical statistics. Applied probability statistics section
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 325 S. graph. Darst. |
| ISBN: | 0471100765 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804114531191881728 |
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| adam_text | Titel: Comparative statistical inference
Autor: Barnett, Vic
Jahr: 1982
Contents Preface vii Preface to Second Edition xi CHAPTER 1 INTRODUCTION: STATISTICAL INFERENCE AND DECISION-MAKING 1 1.1 What is Statistics? 1 1.2 Probability models 4 1.3 Relevant information 1 1.4 Statistical inference and decision-making 13 1.5 Different approaches 16 1.6 Arbitrariness and controversy 19 1.7 Historical comment and further references 23 References 26 CHAPTER 2 AN ILLUSTRATION OF THE DIFFERENT APPROACHES 28 2.1 A practical example 28 2.2 Sample data as the sole source of information: the classical approach 31 2.2.1 Batch quality 32 2.2.2 Component lifetimes 42 2.3 Relevant prior information: the Bayesian approach 45 2.3.1 Prior information on batch quality 46 2.3.2 Prior attitudes about component lifetimes! 51 2.4 Costs and consequences: simple decision theory ideas 53 2.5 Comment and comparisons 61 References 62 CHAPTER 3 PROBABILITY 64 3.1 Types of probability 64 3.2 ‘ Classical’ probability 73 3.3 The frequency view 75
XIV CONTENTS 3.4 Logical probability 80 3.5 Subjective probability 84 3.6 Other viewpoints 91 3.7 Some historical background 92 3.8 And so . . . 93 3.9 And yet ... 94 References 94 CHAPTER 4 UTILITY AND DECISION-MAKING 96 4.1 Setting a value on rewards and consequences 98 4.2 The rational expression of preferences 103 4.3 Preferences for prospects and mixtures of prospects 104 4.4 The numerical assessment of prospects 106 4.5 The measurement of utilities 108 4.5.1 Formal construction of utilities 108 4.5.2 Personal expression of utilities 110 4.6 Decision-making 111 4.7 The utility of money 112 4.8 Comment: mathematical refinements: distinctions of attitude 115 References 117 CHAPTER 5 CLASSICAL INFERENCE 119 5.1 Basic aims and concepts 121 5.1.1 Information and its representation 123 5.2 Estimation and testing hypotheses—the dual aims 127 5.3 Point estimation 132 5.3.1 Criteria for point estimators 133 5.3.2 Optimum estimators 139 5.3.3 Methods of constructing estimators 146 5.3.4 Estimating several parameters 154 5.4 Testing statistical hypotheses 157 5.4.1 Criteria for hypothesis tests 157 5.4.2 Uniformly most powerful tests 162 5.4.3 Construction of tests 169 5.5 Region and interval estimates 172 5.6 Ancillarity, conditionality, modified forms of sufficiency and likelihood 176 5.7 Comment and controversy 180 5.7.1 Initial and final precision 181 5.7.2 Hypothesis tests and decisions 184 5.7.3 Counter criticism 185 References 188
CONTENTS XV CHAPTER 6 BAYESIAN INFERENCE 190 6.1 Thomas Bayes 190 6.2 The Bayesian method 192 6.3 Particular techniques 196 6.4 PWor ignorance 206 6.5 Vague prior knowledge 209 6.6 Substantial prior knowledge 211 6.6.1 Conjugate prior distributions 213 6.7 Empirical Bayes methods; meta-prior distributions 217 6.7.1 Empirical Bayes methods 218 6.7.2 Meta-prior distributions 220 6.8 Comment and controversy 222 6.8.1 Interpretation of prior and posterior distributions 222 6.8.2 Sufficiency, likelihood and unbiasedness 225 6.8.3 Controversy 226 References 228 CHAPTER 7 DECISION THEORY 231 7.1 /1« illustrative example 233 7.2 Rai/c concepts and principles 242 7.2.1 The decision theory model 244 7.2.2 The no-data situation 244 7.2.3 Sample data 245 7.3 Attainment and implementation 249 7.3.1 Admissibility and unbiasedness 250 7.3.2 Determination of Bayes decision rules 254 7.3.3 Minimax decision rules 258 7.3.4 Estimation and hypothesis testing 258 7.4 Problems with finite numbers of actions, and states of nature 263 7.4.1 The no-data problem 263 7.4.2 The use of sample data 265 7.5 Extensions and modifications 266 7.6 Critical comment 269 References 271 CHAPTER 8 SOME OTHER APPROACHES 273 8.1 Fiducial injerence 274 8.2 Likelihood injerence 282 8.3 Plausibility injerence 287 8.4 Structural injerence 289 8.5 Pivotal inference 296 8.6 Information 298
XVI CONTENTS 8.7 The ‘Mathematics of Philosophy 301 References 303 CHAPTER 9 PERSPECTIVE 305 References 309 Bibliography 311 Subject and Author Index 315
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| author | Barnett, Vic 1938- |
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| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| indexdate | 2024-07-09T15:08:12Z |
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| isbn | 0471100765 |
| language | English |
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| series2 | Wiley series in probability and mathematical statistics. Applied probability statistics section |
| spelling | Barnett, Vic 1938- Verfasser (DE-588)131393308 aut Comparative statistical inference Vic Barnett 2. ed. Chichester [u.a.] Wiley 1982 XVI, 325 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and mathematical statistics. Applied probability statistics section Inferenzstatistik (DE-588)4247120-5 gnd rswk-swf Statistische Entscheidungstheorie (DE-588)4077850-2 gnd rswk-swf Statistische Schlussweise (DE-588)4182963-3 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Statistische Entscheidungstheorie (DE-588)4077850-2 s DE-604 Inferenzstatistik (DE-588)4247120-5 s 2\p DE-604 Statistische Schlussweise (DE-588)4182963-3 s 3\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000034510&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 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Barnett, Vic 1938- Comparative statistical inference Inferenzstatistik (DE-588)4247120-5 gnd Statistische Entscheidungstheorie (DE-588)4077850-2 gnd Statistische Schlussweise (DE-588)4182963-3 gnd |
| subject_GND | (DE-588)4247120-5 (DE-588)4077850-2 (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 | Inferenzstatistik (DE-588)4247120-5 gnd Statistische Entscheidungstheorie (DE-588)4077850-2 gnd Statistische Schlussweise (DE-588)4182963-3 gnd |
| topic_facet | Inferenzstatistik Statistische Entscheidungstheorie Statistische Schlussweise Einführung |
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