Convergence rates of posterior distributions for dirichlet mixtures of normal densities.

In this paper convergence rates of posterior distributions of Ulrich-let mixtures of normal densities are determined when the true density is a mixture of normals over a compact set of locations. The scale parameter is allowed to take on values in an interval (O, σ2), with σ2 known. For location mixtures the rate depends on the tail behavior of the base measure as well as on the tail behavior of the prior for the scale parameter. For location-scale mixtures, if the location and scale parameters are independently distributed according to Dirichlet processes, then the rate depends on the tail behavior of the base measures. If the scale and location parameters are components of the overall mixing parameter, then the rate is governed by the tail behavior of the base measure of the unique Dirichlet process prior.