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

2009.

Research output: Working paper

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

2009.

Research output: Working paper

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Shafer, Glenn ; Shen, Alexander ; Vereshchagin, Nikolai ; Vovk, Vladimir. / Test martingales, Bayes factors, and p-values. 2009.

BibTeX

@techreport{d9ecf99b305b4898a1817af120beabe1,
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",
year = "2009",
month = dec,
day = "21",
language = "English",
type = "WorkingPaper",

}

RIS

TY - UNPB

T1 - Test martingales, Bayes factors, and p-values

AU - Shafer, Glenn

AU - Shen, Alexander

AU - Vereshchagin, Nikolai

AU - Vovk, Vladimir

N1 - 15 pages

PY - 2009/12/21

Y1 - 2009/12/21

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.

AB - 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.

KW - math.ST

KW - stat.TH

KW - 62A01

M3 - Working paper

BT - Test martingales, Bayes factors, and p-values

ER -