February 2008
This article focuses on the problem of choosing a prior for a probability measure characterizing the joint distribution of multiple subject-specific parameters within a Bayesian hierarchical model. A local partition process prior is proposed, which has large support and induces dependent, local clustering. Subjects can be clustered together for a subset of their parameters, and one learns about similarities between subjects increasingly as parameters are added. The local partition process prior is constructed through a locally-weighted mixture of global and local components, resulting in a generalization of joint and independent Dirichlet process priors. Some basic properties of the process are described, including simple two-parameter expressions for marginal and conditional clustering probabilities. A slice sampler is developed which bypasses the need to approximate the countably infinite random measure in performing posterior computation. The methods are illustrated using simulation examples, and an application to hormone trajectory data from an epidemiologic study.
Keywords: Dirichlet process; Functional data; Local shrinkage; Meta analysis; Multi-task learning; Partition model; Slice sampling; Stick-breaking.
The manuscript is available in PDF formats.