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

Statistical Science. 2011. Vol. 26. No. 1. P. 84-101.
Shafer G., Shen A., Vereshchagin N., Vovk V.

A nonnegative martingale with initial value equal to one mea- sures 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.