A mathematical theory of arguments for statistical evidence

Auteurs

• André-Paul Weber

Paramètres

• Informatique, programmation
• Contributions to statistics

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This book explores reasoning under uncertainty based on statistical evidence, focusing on the search for arguments supporting or opposing specific hypotheses. It comprises two key aspects: the first draws from classical formal logic, where deductions stem from a knowledge base of observed facts and domain-specific formulas. Here, statistical observations serve as the facts, while general knowledge is represented by a type of statistical model known as functional models. The second aspect addresses the uncertainty inherent in formal reasoning, utilizing the theory of hints. This approach assumes that an uncertain perturbation takes a specific value, allowing for logical evaluation of the resulting consequences. Consequently, the original uncertainty is transferred to the implications of this assumption, a process termed assumption-based reasoning. Before delving into the book's content, it is worthwhile to examine the historical roots of assumption-based reasoning within the statistical framework. In 1930, R. A. Fisher introduced the concept of fiducial distribution as a new form of argument, contrasting it with the traditional Bayesian argument, thereby laying foundational ideas that inform the discussions in this work.

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• Année de publication: 2002