Nonparametric Bayes Estimation with Incomplete Dirichlet Prior Information.
Gregory Campbell, Myles Hollander · 1977
Typically, to use estimators which are Bayes with respect to Ferguson's Dirichlet process prior, the statistician must provide a complete specification of the process parameter alpha, a non-negative non-null finite measure on a measureable space (X, A). Here we take X = R, the real line, and A = B the Borel sigma-field. Mixed rules (rules which minimize the average maximum risk) are derived for estimating Pr(X or = Y) and for estimating rank order. These estimators are incomplete information analogues of Fergusons Bayes estimator of Pr(X or = Y) and the Campbell-Hollander Bayes estimator of rank order.