Probability Matching Priors For One-Way Unbalanced Random Effect Models

초록

This paper considers development of noninformative priors for unbalanced one-way random effect models when the parameter of interest is the ratio of variance components. Several priors including Jeffreys prior, the two-group reference prior of Bernardo (1979), the one-at-a-time reference prior of Berger and Bernardo (1992a,b) and several priors introduced by Chaloner (1987) are compared according to the probability matching criterion. First order probability matching priors are those for which the coverage probabilities of Bayesian credible intervals match asymptotically their frequentist counterparts up to o(l/N1/2), where N is the rate at which the information grows on the parameter under consideration. Under a suitable orthogonal reparameterization (Cox and Reid, 1987), it is possible to characterize the class of first order probability matching priors. However, it is shown that there does not exist any second order probability matching prior in this case. Based on the matching criterion, two-group, one-at-a-time, Jeffreys' prior, parametric orthogonality, our recommended prior is the one-at-a-time reference prior which works well even for moderately large sample sizes. © 2002, Oldenbourg Wissenschaftsverlag GmbH, Rosenheimer Str. 145, 81671 München. All rights reserved.

키워드