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

In: Statistical Science, Vol. 26, 2011, p. 84 - 101.

Research output: Contribution to journalArticlepeer-review

Published

Standard

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

In: Statistical Science, Vol. 26, 2011, p. 84 - 101.

Research output: Contribution to journalArticlepeer-review

Harvard

Shafer, G, Shen, A, Vereshchagin, N & Vovk, V 2011, 'Test martingales, Bayes factors, and p-values', Statistical Science, vol. 26, pp. 84 - 101.

APA

Shafer, G., Shen, A., Vereshchagin, N., & Vovk, V. (2011). Test martingales, Bayes factors, and p-values. Statistical Science, 26, 84 - 101.

Vancouver

Shafer G, Shen A, Vereshchagin N, Vovk V. Test martingales, Bayes factors, and p-values. Statistical Science. 2011;26:84 - 101.

Author

Shafer, Glenn ; Shen, Alexander ; Vereshchagin, Nikolai ; Vovk, Vladimir. / Test martingales, Bayes factors, and p-values. In: Statistical Science. 2011 ; Vol. 26. pp. 84 - 101.

BibTeX

@article{1d6d46ee1be94d74abaf5933dae7227b,
title = "Test martingales, Bayes factors, and p-values",
abstract = "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.",
author = "Glenn Shafer and Alexander Shen and Nikolai Vereshchagin and Vladimir Vovk",
year = "2011",
language = "English",
volume = "26",
pages = "84 -- 101",
journal = "Statistical Science",
issn = "0883-4237",
publisher = "Institute of Mathematical Statistics",

}

RIS

TY - JOUR

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

AU - Shafer, Glenn

AU - Shen, Alexander

AU - Vereshchagin, Nikolai

AU - Vovk, Vladimir

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

M3 - Article

VL - 26

SP - 84

EP - 101

JO - Statistical Science

JF - Statistical Science

SN - 0883-4237

ER -