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 p-value. We give a simple characterization of all increasing functions that eliminate the exaggeration.
Original language | English (US) |
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Pages (from-to) | 84-101 |
Number of pages | 18 |
Journal | Statistical Science |
Volume | 26 |
Issue number | 1 |
DOIs | |
State | Published - 2011 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Mathematics(all)
- Statistics, Probability and Uncertainty
Keywords
- Bayes factors
- Evidence
- Hypothesis testing
- Martingales
- p-values