"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"--
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 Statisticians 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 Savages 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.
1.
1. Philosophical Theories of Knowledge and Truth. 2 Deduction and
Induction.
3. Hilberts 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 Savages 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.
Yudi Pawitan graduated with a PhD in statistics in 1987 from the University of California at Davis and has been a professor of biostatistics since 2001 at the Department of Medical Epidemiology and Biostatistics, Karolinska Institutet, Stockholm, Sweden. He has worked in many areas of statistical applications, including time series analyses and medical imaging, and for the last 20 years in the modelling and analysis of high-throughput genetic and molecular data with applications in cancer. He has published more than 200 peer-reviewed research papers, split about equally between methodology and applied publications. He is the author of the monograph In All Likelihood (2001) and co-author of Generalized Linear Models with Random Effects (2017) together with Youngjo Lee and John Nelder, both covering likelihood-based statistical modelling and inference. Philosophy of science, statistical puzzles and paradoxes have been lifelong interests.
Youngjo Lee graduated with a PhD in statistics in 1983 from Iowa State University. He is currently a professor emeritus of statistics at Seoul National University, an endowed-chair professor of data and knowledge service engineering at Dankook University, and a vice president of the Korean Academy of Science and Technology. Alongside the late John Asworth Nelder, he is an originator of hierarchical generalized models and h-likelihood, having co-authored over 200 peer-reviewed research papers on the application of h-likelihood in various statistical areas. He is also a co-author of monographs on h-likelihood theory and applications. Furthermore, he has developed related software and is currently extending h-likelihood procedures to deep neural networks.
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