Modelling and computation using NCoRM mixtures for density regression

Normalized compound random measures are flexible nonparametric priors for related distributions. We consider building general nonparametric regression models using normalized compound random measure mixture models. We develop a general approach to the unbiased estimation of Laplace functionals of compound random measure (which includes completely random measures as a special case). This allows us to propose a novel pseudo-marginal Metropolis-Hastings sampler for normalized compound random measure mixture models. The approach is illustrated on problems of density regression.