E.T. Jaynes's 'Probability Theory: The Logic of Science' offers a comprehensive and rigorous treatment of probability theory, emphasizing its logical foundations. Jaynes argues that probability is not merely a measure of subjective belief or long-run frequencies, but rather a framework for logical reasoning under conditions of incomplete information. The book presents a coherent and consistent approach to probability, integrating Bayesian methods and emphasizing the importance of prior knowledge in statistical inference. It challenges traditional frequentist interpretations and provides a powerful alternative for scientific modeling and decision-making. Jaynes's work has had a profound impact on various fields, including physics, statistics, and artificial intelligence.
There is a logical flaw in the statistical methods used across experimental science. This fault is not a minor academic quibble: it underlies a reproducibility crisis now threatening entire disciplines. In an increasingly statistics-reliant society, this same deeply rooted error shapes decisions in medicine, law, and public policy with profound consequences. The foundation of the problem is a misunderstanding of probability and its role in making inferences from observations.
Aubrey Clayton traces the history of how statistics went astray, beginning with the groundbreaking work of the seventeenth-century mathematician Jacob Bernoulli and winding through gambling, astronomy, and genetics. Clayton recounts the feuds among rival schools of statistics, exploring the surprisingly human problems that gave rise to the discipline and the all-too-human shortcomings that derailed it. He highlights how influential nineteenth- and twentieth-century figures developed a statistical methodology they claimed was purely objective in order to silence critics of their political agendas, including eugenics.
Clayton provides a clear account of the mathematics and logic of probability, conveying complex concepts accessibly for readers interested in the statistical methods that frame our understanding of the world. He contends that we need to take a Bayesian approach--that is, to incorporate prior knowledge when reasoning with incomplete information--in order to resolve the crisis. Ranging across math, philosophy, and culture, Bernoulli's Fallacy: Statistical Illogic and the Crisis of Modern Science (Columbia UP, 2021) explains why something has gone wrong with how we use data--and how to fix it.
Galina Limorenko is a doctoral candidate in Neuroscience with a focus on biochemistry and molecular biology of neurodegenerative diseases at EPFL in Switzerland.
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New Books in Mathematics 