  We develop a scalable multi-step Monte Carlo algorithm for inference under a
large class of nonparametric Bayesian models for clustering and classification.
Each step is "embarrassingly parallel" and can be implemented using the same
Markov chain Monte Carlo sampler. The simplicity and generality of our approach
makes inference for a wide range of Bayesian nonparametric mixture models
applicable to large datasets. Specifically, we apply the approach to inference
under a product partition model with regression on covariates. We show results
for inference with two motivating data sets: a large set of electronic health
records (EHR) and a bank telemarketing dataset. We find interesting clusters
and favorable classification performance relative to other widely used
competing classifiers.
