Stein’s method for the Poisson–Dirichlet distribution and the Ewens sampling formula, with applications to Wright–Fisher models

We provide a general theorem bounding the error in approximation of random measure interest—for example, empirical population types Wright–Fisher model—and Dirichlet process, which is having Poisson–Dirichlet distributed atoms with i.i.d. labels from diffuse distribution. The implicit metric captures sizes and locations masses, so also yields bounds on between masses interest apply result to bound stationary distribution finite model infinite-alleles mutation structure (not necessarily parent independent) by An important consequence our an explicit upper total variation distance partition generated sampling distribution, Ewens formula. small if sample size n much smaller than N1/6log(N)−1/2, where N size. Our analysis requires separate interest, giving second moment number follows new development Stein’s method for viewing process as Fleming–Viot then applying Barbour’s generator approach.