**Test martingales, Bayes factors, and p-values.** / Shafer, Glenn; Shen, Alexander; Vereshchagin, Nikolai; Vovk, Vladimir.

Research output: Working paper

Published

**Test martingales, Bayes factors, and p-values.** / Shafer, Glenn; Shen, Alexander; Vereshchagin, Nikolai; Vovk, Vladimir.

Research output: Working paper

Shafer, G., Shen, A., Vereshchagin, N., & Vovk, V. (2009). *Test martingales, Bayes factors, and p-values*.

Shafer G, Shen A, Vereshchagin N, Vovk V. Test martingales, Bayes factors, and p-values. 2009 Dec 21.

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title = "Test martingales, Bayes factors, and p-values",

abstract = "A nonnegative martingale with initial value equal to one measures the evidence against a probabilistic hypothesis. The inverse of its value at some stopping time can be interpreted as a Bayes factor. It can be shown that if we exaggerate the evidence by considering the largest value attained so far by such a martingale, the exaggeration will not be great, 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.",

keywords = "math.ST, stat.TH, 62A01",

author = "Glenn Shafer and Alexander Shen and Nikolai Vereshchagin and Vladimir Vovk",

note = "15 pages",

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month = dec,

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N2 - A nonnegative martingale with initial value equal to one measures the evidence against a probabilistic hypothesis. The inverse of its value at some stopping time can be interpreted as a Bayes factor. It can be shown that if we exaggerate the evidence by considering the largest value attained so far by such a martingale, the exaggeration will not be great, 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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