Preface |
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xi | (4) |
Preface to Second Edition |
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xv | (2) |
Preface to Third Edition |
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xvii | (2) |
Acknowledgements |
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xix | |
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Chapter 1. Introduction: Statistical Inference and Decision-making |
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1 | (28) |
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1 | (3) |
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4 | (3) |
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7 | (6) |
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1.4 Statistical Inference and Decision-making |
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13 | (2) |
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15 | (4) |
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1.6 Arbitrariness and Controversy |
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19 | (4) |
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1.7 Historical Comment and Further References |
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23 | (6) |
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Chapter 2. An Illustration of the Different Approaches |
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29 | (36) |
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29 | (3) |
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2.2 Sample Data as the Sole Source of Information: the Classical Approach |
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32 | (15) |
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33 | (10) |
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2.2.2 Component Lifetimes |
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43 | (4) |
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2.3 Relevant Prior Information: the Bayesian Approach |
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47 | (7) |
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2.3.1 Prior Information on Batch Quality |
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47 | (6) |
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2.3.2 Prior Attitudes about Component Lifetimes |
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53 | (1) |
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2.4 Costs and Consequences: Simple Decision Theory Ideas |
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54 | (8) |
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2.5 Comment and Comparisons |
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62 | (3) |
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65 | (34) |
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65 | (8) |
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3.2 'Classical' Probability |
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73 | (3) |
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76 | (5) |
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81 | (3) |
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3.5 Subjective Probability |
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84 | (8) |
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92 | (4) |
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92 | (2) |
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94 | (1) |
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3.6.3 Risk, Uncertainty and Sensitivity Analysis |
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95 | (1) |
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3.7 Some Historical Background |
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96 | (1) |
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97 | (1) |
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98 | (1) |
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Chapter 4. Utility and Decision-making |
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99 | (24) |
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4.1 Setting a Value on Rewards and Consequences |
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101 | (5) |
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4.2 The Rational Expression of Preferences |
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106 | (2) |
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4.3 Preferences for Prospects and Mixtures of Prospects |
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108 | (2) |
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4.4 The Numerical Assessment of Prospects |
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110 | (1) |
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4.5 The Measurement of Utilities |
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111 | (4) |
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4.5.1 Formal Construction of Utilities |
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111 | (2) |
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4.5.2 Personal Expression of Utilities |
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113 | (2) |
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115 | (1) |
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116 | (3) |
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4.8 Comment: Mathematical Refinements: Distinctions of Attitude |
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119 | (4) |
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Chapter 5. Classical Inference |
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123 | (78) |
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5.1 Basic Aims and Concepts |
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125 | (6) |
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5.1.1 Information and its Representation |
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127 | (4) |
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5.2 Estimation and Testing Hypotheses--the Dual Aims |
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131 | (6) |
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137 | (28) |
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5.3.1 Criteria for Point Estimators |
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137 | (7) |
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144 | (8) |
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5.3.3 Methods of Constructing Estimators |
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152 | (10) |
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5.3.4 Estimating Several Parameters |
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162 | (3) |
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5.4 Testing Statistical Hypotheses |
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165 | (16) |
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5.4.1 Criteria for Hypothesis Tests |
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166 | (5) |
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5.4.2 Uniformly Most Powerful Tests |
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171 | (6) |
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5.4.3 Construction of Tests |
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177 | (4) |
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5.5 Region and Interval Estimates |
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181 | (4) |
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5.6 Ancillarity, Conditionality, Modified forms of Sufficiency and Likelihood |
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185 | (6) |
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5.6.1 The Sufficiency, Conditionality and Likelihood Principles |
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186 | (3) |
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5.6.2 Modified Likelihood Forms (Marginal, Partial, Profile, etc.) |
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189 | (2) |
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5.7 Comment and Controversy |
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191 | (10) |
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5.7.1 Initial and Final Precision |
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192 | (2) |
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5.7.2 Prediction and Tolerance Regions |
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194 | (1) |
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5.7.3 Hypothesis Tests and Decisions |
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195 | (2) |
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197 | (4) |
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Chapter 6. Bayesian Inference |
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201 | (50) |
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201 | (2) |
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203 | (4) |
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6.3 Particular Techniques |
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207 | (10) |
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6.4 Prediction in Bayesian Inference |
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217 | (2) |
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219 | (16) |
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220 | (5) |
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6.5.2 Vague Prior Knowledge |
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225 | (3) |
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6.5.3 Substantial Prior Knowledge |
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228 | (2) |
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6.5.4 Conjugate Prior Distributions |
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230 | (4) |
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6.5.5 Quantifying Subjective Prior Information |
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234 | (1) |
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6.6 Computing Posterior Distributions |
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235 | (3) |
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6.7 Empirical Bayes' methods: Meta-prior Distributions |
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238 | (4) |
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6.7.1 Empirical Bayes' Methods |
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238 | (2) |
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6.7.2 Meta-prior Distributions |
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240 | (2) |
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6.8 Comment and Controversy |
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242 | (9) |
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6.8.1 Interpretation of Prior and Posterior Distributions |
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242 | (3) |
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6.8.2 Sufficiency, Likelihood and Unbiasedness |
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245 | (2) |
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247 | (4) |
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Chapter 7. Decision Theory |
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251 | (46) |
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7.1 An Illustrative Example |
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253 | (9) |
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7.2 Basic Concepts and Principles |
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262 | (7) |
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7.2.1 The Decision Theory Model |
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264 | (1) |
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7.2.2 The No-data Situation |
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264 | (1) |
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265 | (4) |
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7.3 Attainment and Implementation |
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269 | (17) |
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7.3.1 Admissibility and Unbiasedness |
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270 | (5) |
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7.3.2 Determination of Bayes' Decision Rules |
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275 | (3) |
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7.3.3 Minimax Decision Rules |
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278 | (1) |
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7.3.4 Estimation and Hypothesis Testing |
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279 | (7) |
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7.4 Problems with Finite Numbers of Actions, and States of Nature |
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286 | (3) |
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7.4.1 The No-data Problem |
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286 | (1) |
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7.4.2 The Use of Sample Data |
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287 | (2) |
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7.5 Extensions and Modifications |
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289 | (3) |
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292 | (5) |
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Chapter 8. Other Approaches |
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297 | (34) |
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298 | (8) |
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306 | (5) |
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8.3 Plausibility Inference |
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311 | (2) |
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313 | (6) |
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319 | (3) |
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322 | (3) |
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325 | (1) |
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8.8 Prequential Inference |
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326 | (1) |
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8.9 Indeterminism and the 'Mathematics of Philosophy' |
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327 | (4) |
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331 | (6) |
References |
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337 | (28) |
Index |
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365 | |