Noninformative Priors for Linear Combination of the Independent Normal Means

다국어 초록 (Multilingual Abstract)

In this paper, we develop the matching priors and the reference priors forlinear combination of the means under the normal populations with equalvariances. We prove that the matching priors are actually the second ordermatching priors and reveal that the second order matching priors match al-ternative coverage probabilities up to the second order (Mukerjee and Reid,1999) and also, are HPD matching priors. It turns out that among all of thereference priors, one-at-a-time reference prior satises a second order match-ing criterion. Our simulation study indicates that one-at-a-time referenceprior performs better than the other reference priors in terms of matching thetarget coverage probabilities in a frequentist sense. We compute Bayesiancredible intervals for linear combination of the means based on the referencepriors.AMS 2000 subject classications.Primary 62F15; Secondary 62F25.Keywords.Probability matching priors, alternative coverage probabilities, HPD match-ing priors, reference priors, linear combination of the means.1. IntroductionConsider observationsYij fromI normal populations specied by the followingmodel:Yij = i + ij ; fori = 1 ;:;I and j = 1 ;:;J; (1.1)Received March 2003; accepted February 2004.

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