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

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

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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.
Original languageEnglish
Pages (from-to)84 - 101
Number of pages17
JournalStatistical Science
Volume26
Publication statusPublished - 2011
This open access research output is licenced under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.

ID: 1336119