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

Research output: Contribution to journal › Article › peer-review

Published

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

Research output: Contribution to journal › Article › peer-review

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

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

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

@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",

}

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 -