Shafer, Glenn, Shen, Alexander, Vereshchagin, Nikolai and Vovk, Vladimir (2011) Test martingales, Bayes factors, and p-values. Statistical Science, 26
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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.
This is a Submitted version This version's date is: 2011 This item is not peer reviewed
https://repository.royalholloway.ac.uk/items/ff4b07dd-1845-cc2e-57fb-c8d95ea6ec73/1/
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