New axioms for rigorous Bayesian probability

2009/08/31 by Maurice J. Dupré, Frank J. Tipler · 1 citation
Physics and Astronomy · Computer Science · Mathematics · #Statistical Mechanics and Entropy #Bayesian Modeling and Causal Inference #Probability and Statistical Research

paper · pdf · doi:10.1214/09-ba422

openalex publication_date 2009/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/26

Abstract

By basing Bayesian probability theory on five axioms, we can give a trivial proof of Cox's Theorem on the product rule and sum rule for conditional plausibility without assuming continuity or differentiablity of plausibility. Instead, we extend the notion of plausibility to apply to unknowns, giving them plausible values. Thus, we combine the best aspects of two approaches to Bayesian probability theory, namely the Cox-Jaynes theory and the de Finetti theory.

Citations

• A Counter Example to Theorems of Cox and Fine
• The Cox Theorem: Unknowns And Plausible Value

Cited by

• Bayesian probability [wikipedia]

Related

• Cox's Theorem and the Jaynesian Interpretation of Probability
• The Cox Theorem: Unknowns And Plausible Value
• What is the plausibility of probability?(revised 2003, 2015)
• Probability Theory without Bayes' Rule
• A Mathematical Theory of Evidence