Philosophies, Puzzles and Paradoxes
A Statistician’s Search for Truth
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ISBN
9781032377391
Bindwijze
Paperback
Taal
Engels
Auteur
Uitgeverij
Chapman & Hall/Crc
Jaar van uitgifte
2024
Aantal pagina's
331
Waar gaat het over?
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.
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
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