Open Access
February 2011 Test Martingales, Bayes Factors and p-Values
Glenn Shafer, Alexander Shen, Nikolai Vereshchagin, Vladimir Vovk
Statist. Sci. 26(1): 84-101 (February 2011). DOI: 10.1214/10-STS347


A nonnegative martingale with initial value equal to one measures evidence against a probabilistic hypothesis. The inverse of its value at some stopping time can be interpreted as a Bayes factor. If we exaggerate the evidence by considering the largest value attained so far by such a martingale, the exaggeration will be limited, and there are systematic ways to eliminate it. The inverse of the exaggerated value at some stopping time can be interpreted as a p-value. We give a simple characterization of all increasing functions that eliminate the exaggeration.


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Glenn Shafer. Alexander Shen. Nikolai Vereshchagin. Vladimir Vovk. "Test Martingales, Bayes Factors and p-Values." Statist. Sci. 26 (1) 84 - 101, February 2011.


Published: February 2011
First available in Project Euclid: 9 June 2011

zbMATH: 1219.62050
MathSciNet: MR2849911
Digital Object Identifier: 10.1214/10-STS347

Keywords: Bayes factors , evidence , Hypothesis testing , Martingales , P-values

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.26 • No. 1 • February 2011
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