Anderson, Robert F. - In: Statistics & Probability Letters 2 (1984) 3, pp. 147-157
Let d[gamma](k(t), t) be the Bayes estimate of the rate of a Poisson process with Gamma prior and loss function [gamma] - d[gamma], l [less-than-or-equals, slant] [gamma] < [infinity]. Let . It is shown that d[gamma] (k(t), t) is a submartingale for l < [gamma] < 2, a martingale for [gamma] = 2 and a supermartingale for [gamma] > 2 with respect to .