Test Martingales, Bayes Factors and $p$-Values
Statistics Theory
2011-06-17 v3 Methodology
Statistics Theory
Abstract
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 -value. We give a simple characterization of all increasing functions that eliminate the exaggeration.
Cite
@article{arxiv.0912.4269,
title = {Test Martingales, Bayes Factors and $p$-Values},
author = {Glenn Shafer and Alexander Shen and Nikolai Vereshchagin and Vladimir Vovk},
journal= {arXiv preprint arXiv:0912.4269},
year = {2011}
}
Comments
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)