| Description |
1 online resource (352 p.) |
| Contents |
Cover -- Half Title -- Title Page -- Copyright Page -- Contents -- Foreword -- Preface -- List of Abbreviations -- List of Puzzles and Paradoxes -- Introduction and Summary -- I. How Do We Know What We Believe Is True? -- 1. Philosophical Theories of Knowledge and Truth -- 1.1. The Rationalists -- 1.2. The Empiricists -- 1.3. The Positivists and the Verification Principle -- 2. Deduction and Induction -- 2.1. Reasoning Solely Based on Induction -- 2.2. Reasoning Solely Based on Deduction -- 2.3. Complementary Induction and Deduction -- 2.4. Abduction -- 2.5. Category-Based Induction |
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3. Hilbert's Broken Dream: Limitations of Deductive Reasoning -- 3.1. Is Euclidean Geometry True? -- 3.2. Gödel's Incompleteness Theorems -- 4. 'Real' Scientific Process -- 4.1. Theory vs Observations -- 4.2. Paradigm Shift -- II. Probability and Inverse-Probability Inference -- 5. The Rise of Probability -- 5.1. Mathematical Probability -- 5.2. Countable vs Finite Additivity -- 5.3. What Is Probability? -- 5.4. Pascal's Wager -- 6. Philosophical Theories of Probability -- 6.1. Classical Theory -- 6.2. Logical Theory -- 6.3. Frequency Theory -- 6.4. Propensity Theory -- 6.5. Subjective Theory |
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6.6. Consensus theory -- 7. Rereading Savage -- 7.1. The Axioms -- 7.2. Qualitative Probability and Axiom 6 -- 7.3. Conditional Probability -- 7.4. Utility, Axiom 7 and The Theorem -- 7.5. Discussion -- 8. The Inverse Probability Method -- 8.1. Bayes's Essay -- 8.2. Bayesian Learning -- 8.3. Laplace's Memoir -- 8.4. Testimony Puzzle -- 8.5. The Sunrise Problem -- 8.6. Qualitative Plausible Reasoning -- 9. What Prior? -- 9.1. The Principle of Insufficient Reason: Uniform Prior -- 9.2. Axiomatic Basis of the Principle of Insufficient Reason -- 9.3. Invariant Prior∗ -- 9.4. Multiparameter Case∗ |
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III. Likelihood and Likelihood-Based Inference -- 10. Likelihood -- 10.1. Classical Likelihood -- 10.2. Exchange Paradox -- 10.3. Prosecutor's Fallacy -- 10.4. Likelihood Principle -- 10.5. Controversy -- 11. P-values and Confidence -- 11.1. Significance Test via Randomization -- 11.2. P-values and Fiducial Probability -- 11.3. Confidence Procedures and Coverage Probability -- 11.4. Can We Say with Complete Confidence that the Sun Will Rise Forever? -- 12. Extended Likelihood -- 12.1. Random Parameters -- 12.2. Hierarchical Likelihood∗ -- 12.3. Confidence Is an Extended Likelihood |
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12.4. Wallet Game Paradox -- 13. Epistemic Confidence -- 13.1. Non-epistemic Confidence and the Dutch Book -- 13.2. Epistemic Confidence Theorem -- 13.3. Epistemic Confidence and Objective Bayesianism -- 13.4. Probability, Likelihood, Extended Likelihood, H-likelihood and Confidence -- IV. Puzzles and Paradoxes -- 14. Paradoxes of Savage's Axioms -- 14.1. Allais's Paradox -- 14.2. Ellsberg's Paradox -- 15. Fallacious Fallacies -- 15.1. Conjunction Fallacy -- 15.2. Inclusion Fallacy -- 15.3. Statistical and Scientific Reasoning -- 15.4. Probability and Likelihood-Based Reasoning |
| Summary |
Aimed at undergraduate students of statistics and researchers interested in the philosophical foundations of statistics. Of interest to philosophers of science, as well as a general audience interested in puzzles and paradoxes |
| Notes |
Description based upon print version of record |
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15.5. Degree of Confirmation |
| Genre/Form |
Electronic books
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| Form |
Electronic book
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| Author |
Lee, Youngjo
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| ISBN |
9781003849032 |
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1003849032 |
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