On the Use of Bayes Factor in Frequentist Testing of a Precise Hypothesis

Author: Chacón J. E.   Montanero J.   Nogales A. G.   Pérez P.  

Publisher: Taylor & Francis Ltd

ISSN: 0361-0926

Source: Communications in Statistics: Theory and Methods, Vol.36, Iss.12, 2007-09, pp. : 2251-2261

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Abstract

This article deals with Bayes factors as useful Bayesian tools in frequentist testing of a precise hypothesis. A result and several examples are included to justify the definition of Bayes factor for point null hypotheses, without merging the initial distribution with a degenerate distribution on the null hypothesis. Of special interest is the problem of testing a proportion (joint with a natural criterion to compare different tests), the possible presence of nuisance parameters, or the influence of Bayesian sufficiency on this problem. The problem of testing a precise hypothesis under a Bayesian perspective is also considered and two alternative methods to deal with are given.