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Biometrika 1998 85(1):55-71; doi:10.1093/biomet/85.1.55
© 1998 by Biometrika Trust
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Reference priors with partial information

D. SUN and J. O. BERGER

Department of Statistics, University of Missouri-Columbia Columbia, Missouri 65211, U.S.A. dsun{at}tat.missouri.edu
Institute of Statistics and Decision Sciences, Duke University Durham, North Carolina 27708, U.S.A. berger{at}tat.duke.edu

In this paper, reference priors are derived for three cases where partial information is available. If a subjective conditional prior is given, two reasonable methods are proposed for finding the marginal reference prior. If, instead, a subjective marginal prior is available, a method for defining the conditional reference prior is proposed. A sufficient condition is then given under which this conditional reference prior agrees with the conditional reference prior derived in the first stage of the reference prior algorithm of Berger & Bernardo (1989, 1992). Finally, under the assumption of independence, a method for finding marginal reference priors is also proposed. Various examples are given to illustrate the methods.

Key Words: Beta distribution • Gamma distribution • Kullback-Leibler divergence • Neyman-Scott problem • Noninformative prior • Normal distribution


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