2009/12/31 by Glenn Shafer, Alexander Shen, Nikolai Vereshchagin +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Bayes factor #Bayes' theorem #Bayesian probability #Exaggeration #Financial Risk and Volatility Modeling #Inverse #Martingale (probability theory) #Optional stopping theorem #Probabilistic logic #Probability and Risk Models #Statistical Distribution Estimation and Applications #Value (mathematics) #math.ST #stat.ME #stat.TH
paper · pdf · doi:10.1214/10-sts347
published as Statistical Science 2011, Vol. 26, No. 1, 84-101 · Published in at http://dx.doi.org/10.1214/10-STS347 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2011/02/01 · arxiv created 2011/06/16 · arxiv updated 2011/06/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.