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Full Description
Unlike mathematics, 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, preferences, assumptions and preconceptions of the interpreter, leading to a variety of interpretations of concepts as well as results. Philosophies, Puzzles and Paradoxes: A Statistician's Search for Truth 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 numerous puzzles and paradoxes and illuminated by extensive discussions of the background philosophy of science.
Features:
Exploration of the philosophy of knowledge and truth and how they relate to deductive and inductive reasoning, and ultimately scientific and statistical thinking
Discussion of the philosophical theories of probability that are wider than the standard Bayesian and frequentist views
Exposition and examination of Savage's axioms as the basis of subjective probability and Bayesian statistics
Explanation of likelihood and likelihood-based inference, including the controversy surrounding the likelihood principle
Discussion of fiducial probability and its evolution to confidence procedure
Introduction of extended and hierarchical likelihood for random parameters, with the recognition of confidence as extended likelihood, leading to epistemic confidence as an objective measure of uncertainty for single events
Detailed analyses and new variations of classic paradoxes, such as the Monty Hall puzzle, the paradox of the ravens, the exchange paradox, and more
Substantive yet non-technical, catering to readers with only introductory exposure to the theory of probability and statistics
This book primarily targets statisticians in general, including both undergraduate and graduate students, as well as researchers interested in the philosophical basis of probability and statistics. It is also suitable for philosophers of science and general readers intrigued by puzzles and paradoxes.
Contents
1. 1. Philosophical Theories of Knowledge and Truth. 2 Deduction and Induction. 3. Hilbert's Broken Dream: Limitations of Deductive Reasoning. 4. 'Real' Scientific Process. 5. The Rise of Probability. 6. Philosophical Theories of Probability. 7. Rereading Savage. 8. Inverse Probability Method. 9. What Prior? 10. Likelihood. 11. P-value and Confidence. 12. Extended Likelihood. 13. Epistemic Confidence. 14. Paradoxes of Savage's Axioms. 15. Fallacious Fallacies. 16. Monty Hall Puzzle and the Three Prisoners Paradox. 17. Lottery Paradox and the Cold Suspect Puzzle. 18. Paradox of the Ravens. 19. Exchange Paradox.
