An Autoregressive Approach to Nonparametric Hierarchical Dependent Modeling

We propose a conditional autoregression framework for a collection of random probability measures. Under this framework, we devise a conditional autoregressive Dirichlet process (DP) that we call one-parameter dependent DP (ω-DDP). The appealing properties of this specification are that it has two equivalent representations and its inference can be implemented in a conditional Polya urn scheme. Moreover, these two representations bear a resemblance to the Polya urn scheme and the stick-breaking representation in the conventional DP. We apply this ω-DDP to Bayesian multivariateresponse regression problems. An efficient Markov chain Monte Carlo algorithm is developed for Bayesian computation and prediction. Our work shows that DPs can be used to handle the computational issue that emerges from other nonparametric Bayesian methods such as Gaussian processes.