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Biometrika 1999 86(2):333-340; doi:10.1093/biomet/86.2.333
© 1999 by Biometrika Trust
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On a property of probability matching priors: matching the alternative coverage probabilities

R MukerjeeA1 and N ReidA2

A1 Indian Institute of Management, Post Box No. 16757, Calcutta 700 027, India E-mail: rmuk1@hotmail.com A2 Department of Statistics, University of Toronto, Toronto, Canada M5S 3G3 E-mail: reid@utstat.utoronot.ca

In frequentist inference based on confidence sets, both the true coverage and the probability for a confidence set to include an alternative value of the parameter of interest are important. Thus if probability matching priors also match such alternative coverage probabilities there is perhaps a stronger justification for calling them noninformative. Considering contiguous alternatives, we obtain the relevant necessary and sufficient conditions. In particular, with n denoting the sample size, it is seen that probability matching priors up to o(n-1/2;) also match the alternative coverage probabilities up to that order while this is not necessarily the case with probability matching priors up to o(n-1).

Key Words: Contiguous alternative; First order; Jeffreys' prior; Noninformative prior; Parametric orthogonality; Second order.


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