A Bayes estimator for ordered parameters and isotonic Bayesian graduation

Abstract

Abstract The problem is to estimate the parameters θ 1 ..., θk under the order restriction θ 1 < ... < θk . A prior distribution is specified such that the probability of the set {(θ 1, ..., θk ): θ 1< ... <θk } is one. This guarantees that the mean of the posterior distribution (Bayes estimator) satisfies the order restriction. This technique, which produces a smoothing effect, is applied to the problem of estimating mortality rates over consecutive age intervals. In this application the result may be viewed as an isotonic Bayesian graduation. A real data example is provided.