Reference Priors With Partial Information

Dongchu Sun and James Berger

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 and Bernardo. Finally, under the assumption of independence, a method for finding marginal reference priors is also proposed. Various examples are given to illustrate the methods. Postscript File (268kB)