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.
"Test Martingales, Bayes Factors and p-Values." Statist. Sci. 26 (1) 84 - 101, February 2011. https://doi.org/10.1214/10-STS347