Test martingales, Bayes factors and \(p\)-values. (English) Zbl 1219.62050

Shafer, Glenn; Shen, Alexander; Vereshchagin, Nikolai; Vovk, Vladimir

Stat. Sci. 26, No. 1, 84-101 (2011).

Summary: 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.

MSC:

62F15	Bayesian inference
60G44	Martingales with continuous parameter
62F03	Parametric hypothesis testing
65C60	Computational problems in statistics (MSC2010)

Keywords:

Bayes factors; evidence; hypothesis testing; martingales; \(p\)-values

Software:

R

References:

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