Isotonic Bayesian Graduation with an Additive Prior

Abstract

Assume the mortality rate at age x + j−1 is q _x +_j−1 = 1− exp(−θj), j = l,…,k. Isotonic Bayesian graduation provides a Bayes estimator of θ ₁ ,… ,θ _k (and consequently, q _x ,…,q _x +k•i) under the assumption θ ₁ < … < θ _k . This is accomplished by specifying a prior distribution for which P(Θ₁ < … < Θ_k) = 1. In a previous paper the prior was defined by where Y ₁ …,Y _k are independent. In this paper the Bayes estimator is developed using the prior The advantages are an easier specification of the prior parameters and shorter computational time.