NONINFORMATIVE PRIORS AND NUISANCE PARAMETERS

We study the conflict between priors that are noninformative for a par ameter of interest versus priors that are noninformative for the whole Parameter. Our investigation leads us to maximize a functional that h as two terms: an asymptotic approximation to a standardized expected K ullback-Leibler distance between the marginal prior and marginal poste rior for a parameter of interest, and a penalty term measuring the dis tance of the prior from the Jeffreys prior. A Positive constant multip lying the second terms determines the tradeoff between noninformativit y for the parameter of interest and noninformativity for the entire pa rameter. As the constant increases, the prior tends to the Jeffreys pr ior. When the constant tends to 0, the prior becomes degenerate except in special cases. This prior does not have a closed-form solution, bu t we present a simple, numerical algorithm for finding the prior. We c ompare this prior to the Berger-Bernardo prior.