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.

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 handling 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, etc.
• Substantive yet non-technical, catering to readers with only introductory exposure to the theory probability and statistics.

This book primarily targets statisticians, 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.