Multivariate kernel partition processes

This article considers the problem of accounting for unknown multivariate mixture distributions within Bayesian hierarchical models motivated by functional data analysis. Most nonparametric Bayes methods rely on global partitioning, with subjects assigned to a single cluster index for all their random effects. We propose a multivariate kernel partition process (KPP) that instead allows the cluster indices to vary. The KPP is shown to be the driving measure for a multivariate ordered Chinese restaurant process, which allows a highly-flexible dependence structure in local clustering. This structure allows the relative locations of the random effects to inform the clustering process, with spatially-proximal random effects likely to be assigned the same cluster index. An efficient exact block Gibbs sampler is developed for posterior computation, avoiding the need to truncate the infinite measure. The methods are applied to functional data analysis, illustrating improvements in model fit, parsimony and predictive performance relative to current methods.