11/2006
This article proposes a class of kernel stick-breaking processes (KSBP) for uncountable collections of dependent random probability measures. The KSBP is constructed by first introducing an infinite sequence of random locations. Independent random probability measures and beta-distributed random weights are assigned to each location. Predictor-dependent random probability measures are then constructed by mixing over the locations, with stick-breaking probabilities expressed as a kernel multiplied by the beta weights. Some theoretical properties of the KSBP are described, including a covariate-dependent prediction rule. A retrospective MCMC algorithm is developed for posterior computation, and the methods are illustrated using a simulated example and an epidemiologic application.
Keywords: Conditional density estimation; Dependent Dirichlet process; Kernel methods; Nonparametric Bayes; Mixture model; Prediction rule; Random partition.
The manuscript is available in PDF formats.