Bayesian Analysis

New axioms for rigorous Bayesian probability

Maurice J. Dupré and Frank J. Tipler

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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.

Article information

Bayesian Anal., Volume 4, Number 3 (2009), 599-606.

First available in Project Euclid: 22 June 2012

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Zentralblatt MATH identifier

Cox de Finetti Jaynes Axiomatic Bayesian Probability Sum Rule Product Rule


Dupré, Maurice J.; Tipler, Frank J. New axioms for rigorous Bayesian probability. Bayesian Anal. 4 (2009), no. 3, 599--606. doi:10.1214/09-BA422.

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