Estimating the Frequency of the Oldest Allele - a Bayesian Approach

Consider an aged-ordered population Zl, Z2, ... , where Z; is the frequency of the ith oldest allele and .EZi = 1. From this population consider an aged-ordered sample of size n with 1 alleles and the frequencies in age-order denoted by M = (/; ml, m2"" ml). vVe calculate the posterior distribution and posterior moments from the population frequency of the oldest allele, Zl, given the sample M, assuming that the population is at stationarity and follows the neutral infinite alleles model. We also calculate the posterior disribution of Zl given a partition of n genes with no age information in the sample. These results are used to determine Bayes estimators for the population frequency of the oldest type, and the analysis is extended to include the posterior distribution of Zl, Z2, ... , Zk given M for any k. nhTfl<?pq' G.E.M. distribution, infinite