Noninformative Priors and Nuisance Parameters

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected].. Taylor & Francis, Ltd. and American Statistical Association are collaborating with JSTOR to digitize, preserve and extend access to Journal of the American Statistical Association. We study the conflict between priors that are noninformative for a parameter of interest versus priors that are noninformative for the whole parameter. Our investigation leads us to maximize a functional that has two terms: an asymptotic approximation to a standardized expected Kullback-Leibler distance between the marginal prior and marginal posterior for a parameter of interest, and a penalty term measuring the distance of the prior from the Jeffreys prior. A positive constant multiplying the second terms determines the tradeoff between noninformativity for the parameter of interest and noninformativity for the entire parameter. As the constant increases, the prior tends to the Jeffreys prior. When the constant tends to 0, the prior becomes degenerate except in special cases. This prior does not have a closed-form solution, but we present a simple, numerical algorithm for finding the prior. We compare this prior to the Berger-Bernardo prior.