Shafer, Glenn, Shen, Alexander, Vereshchagin, Nikolai and Vovk, Vladimir (2009) Test martingales, Bayes factors, and p-values.
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A nonnegative martingale with initial value equal to one measures the evidence against a probabilistic hypothesis. The inverse of its value at some stopping time can be interpreted as a Bayes factor. It can be shown that if we exaggerate the evidence by considering the largest value attained so far by such a martingale, the exaggeration will not be great, 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.
This is a Submitted version This version's date is: 21/12/2009 This item is not peer reviewed
https://repository.royalholloway.ac.uk/items/4d99fd0e-eeb5-69c7-3c08-3c687c0a38bb/6/
Deposited by Research Information System (atira) on 22-Jul-2014 in Royal Holloway Research Online.Last modified on 22-Jul-2014
15 pages