Bayesian Analysis

New axioms for rigorous Bayesian probability

Maurice J. Dupré and Frank J. Tipler

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 22 June 2012

Permanent link to this document
https://projecteuclid.org/euclid.ba/1340369856

Digital Object Identifier
doi:10.1214/09-BA422

Mathematical Reviews number (MathSciNet)
MR2551047

Zentralblatt MATH identifier
1330.62044

Keywords
Cox de Finetti Jaynes Axiomatic Bayesian Probability Sum Rule Product Rule

Citation

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. https://projecteuclid.org/euclid.ba/1340369856


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