Estimating the frequency of the oldest allele: a bayesian approach

In this paper we calculate posterior distributions associated with a version of the Poisson.Dirichlet distribution called the GEM. The GEM has been shown (by several authors) to be the limiting stationary distribution for allele frequencies listed in age order associated with the neutral infinite alleles model. In view of this result, we use our posterior distributions to calculate Bayes estimators for the frequency of the oldest allele given a sample.