Sampling the Dirichlet Mixture Model with Slices

We provide a new approach to the sampling of the well known mixture of Dirichlet process model. Recent attention has focused on retention of the random distribution function in the model, but sampling algorithms have then suffered from the countably infinite representation these distributions have. The key to the algorithm detailed in this paper, which also keeps the random distribution functions, is the introduction of a latent variable which allows a finite number, which is known, of objects to be sampled within each iteration of a Gibbs sampler.Bayesian Nonparametrics, Density estimation, Dirich-let process, Gibbs sampler, Slice sampling.

Asymptotically minimax empirical Bayes estimation of a sparse normal mean vector

For the important classical problem of inference on a sparse high-dimensional normal mean vector, we propose a novel empirical Bayes model that admits a posterior distribution with desirable properties under mild conditions. In particular, our empirical Bayes posterior distribution concentrates on balls, centered at the true mean vector, with squared radius proportional to the minimax rate, and its posterior mean is an asymptotically minimax estimator. We also show that, asymptotically, the support of our empirical Bayes posterior has roughly the same effective dimension as the true sparse mean vector. Simulation from our empirical Bayes posterior is straightforward, and our numerical results demonstrate the quality of our method compared to others having similar large-sample properties.Comment: 18 pages, 3 figures, 3 table