Sequential Importance Sampling for NonparametricBayes Models : The Next GenerationRunning

There are two generations of Gibbs sampling methods for semi-parametric models involving the Dirichlet process. The rst generation suuered from a severe drawback; namely that the locations of the clusters, or groups of parameters, could essentially become xed, moving only rarely. Two strategies that have been proposed to create the second generation of Gibbs samplers are integration and appending a second stage to the Gibbs sampler wherein the cluster locations are moved. We show that these same strategies are easily implemented for the sequential importance sampler, and that the rst strategy dramatically improves results. As in the case of Gibbs sampling, these strategies are applicable to a much wider class of models. They are shown to provide more uniform importance sampling weights and lead to additional Rao-Blackwellization of estimators. There are two generations of Gibbs sampling methods for semi-parametric models involving the Dirichlet process. The rst generation suuered from a severe drawback; namely that the locations of the clusters, or groups of parameters, could essentially become xed, moving only rarely. Two strategies that have been proposed to create the second generation of Gibbs samplers are integration and appending a second stage to the Gibbs sampler wherein the cluster locations are moved. We show that these same strategies are easily implemented for the sequential importance sampler, and that the rst strategy dramatically improves results. As in the case of Gibbs sampling, these strategies are applicable to a much wider class of models. They are shown to provide more uniform importance sampling weights and lead to additional Rao-Blackwellization of estimators.