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Some new results on probability matching priors. (English) Zbl 0986.62017

Summary: The paper has three components. First, for a real-valued parameter of interest orthogonal to the nuisance parameter vector, we find a necessary and sufficient condition for the equivalence of second order quantile matching priors and highest posterior density regions matching priors within the class of first order quantile matching priors. Examples are presented to illustrate the result. Second, we develop a quantile matching prior in a normal hierarchical Bayesian model. This prior turns out to be different from that one proposed earlier by C.N. Morris [Publ. Math. Res. Cent., Univ. Wis. Madison 48, 25-50 (1983; Zbl 0581.62033)]. Third, we obtain an exact matching result when the objective is prediction of a real-valued random variable from a location family of distributions.

MSC:

62F15 Bayesian inference
62F25 Parametric tolerance and confidence regions
62E20 Asymptotic distribution theory in statistics

Citations:

Zbl 0581.62033
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