Philosophies, 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 thinkingDiscussion of the philosophical theories of probability that are wider than the standard Bayesian and frequentist viewsExposition and examination of Savage’s axioms as the basis of subjective probability and Bayesian statisticsExplanation of likelihood and likelihood-based inference, including the controversy surrounding the likelihood principleDiscussion of fiducial probability and its evolution to confidence procedureIntroduction 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 eventsDetailed analyses and new variations of classic paradoxes, such as the Monty Hall puzzle, the paradox of the ravens, the exchange paradox, and moreSubstantive yet non-technical, catering to readers with only introductory exposure to the theory of probability and statisticsThis 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.