Bayesians Versus Frequentists: A Philosophical Debate on Statistical Reasoning

by Jordi Vallverdu

This book analyzes the origins of statistical thinking as well as its related philosophical questions, such as causality, determinism or chance. Bayesian and frequentist approaches are subjected to a historical, cognitive and epistemological analysis, making it possible to not only compare the two competing theories, but to also find a potential solution. The work pursues a naturalistic approach, proceeding from the existence of numerosity in natural environments to the existence of contemporary formulas and methodologies to heuristic pragmatism, a concept introduced in the book’s final section. This monograph will be of interest to philosophers and historians of science and students in related fields. Despite the mathematical nature of the topic, no statistical background is required, making the book a valuable read for anyone interested in the history of statistics and human cognition.

Genres: Philosophy

122 pages, Paperback

First published December 10, 2015

Reviews

[Samuël David · Rating 2 out of 5]

Whilst the author is clearly very knowledgeable of the topic and literature, he could have asked someone to proofread his text or use some simple grammar correction software, let alone review the structure of the book. Keep it on the shelf to cite and as an index for the works he references

[Sarah Pirenne · Rating 3 out of 5]

Broad subjects including infants' first understanding of numbers, quite a lot of general history of philosophy of science etc. Quite chaotic though and the final proclamation of bayesianism as the "winning" paradigm does not match the reality of a pick and choose approach that is generally applied by practitioners (and also supported by the author himself in most of the chapters?).

[Tom Schulte · Rating 4 out of 5]

This book argues for the superiority of bayesianism (the author goes minuscule here) over frequentism in nearly two dozen articles categorized into a few sections with an index of persons. Sections include the origins of numerical and statistical thinking, related philosophical questions, and a contrasting of bayesian and frequentist approaches. The initial, historical section takes a broad view encompassing the cognitive abilities of animals, numerosity (“the ability to appreciate and understand numbers”), and the formation of a foundation for statistics. The middle section presents a brisk overview of statistics from the invention of dice in India to Nineteenth Century formalizations by Peirce, Venn, de Morgan, etc. These two sections prepare the ground for a final culmination in the work of Bayes and the role his approach has had and, by the author, should have. These sections are good, standalone treatments in aspects of the history of mathematics...

[Look for my entire review up at MAA Reviews.]