Philosophies, puzzles and paradoxes a statistician's search for truth
"Mathematics is focused on formal manipulation of abstract concepts, while statistics deals with real-world data and involves a higher degree of subjectivity due to the role of interpretation. Interpretation is shaped by context as well as the knowledge, biases, assumptions or preconceptions of...
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Boca Raton, London, New York
CRC Press
2024
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| Ausgabe: | First edition |
| Schriftenreihe: | A Chapman & Hall book Statistics
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Tag hinzufügen | Zusammenfassung: | "Mathematics is focused on formal manipulation of abstract concepts, while statistics deals with real-world data and involves a higher degree of subjectivity due to the role of interpretation. Interpretation is shaped by context as well as the knowledge, biases, assumptions or preconceptions of the interpreter, leading to a variety of potential interpretations of concepts as well as results. This book thoroughly examines the distinct philosophical approaches to statistics--Bayesian, frequentist, and likelihood--arising from different interpretations of probability and uncertainty. These differences are highlighted through a variety of puzzles and paradoxes"-- 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 -- 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 -- 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∗ -- III. Likelihood and Likelihood-Based Inference -- 10. Likelihood. |
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| Beschreibung: | Enthält Literaturangaben und Index Literaturverzeichnis: Seite 299-310 |
| Beschreibung: | xxvii, 323 Seiten Illustrationen, Diagramme |
| ISBN: | 9781032377391 978-1-032-37739-1 9781032377407 978-1-032-37740-7 |