title: Semiparametric Bayes hierarchical models with mean and variance constraints.
abstract: In parametric hierarchical models, it is standard practice to place mean and variance constraints on the latent variable distributions for the sake of identifiability and interpretability. Because incorporation of such constraints is challenging in semiparametric models that allow latent variable distributions to be unknown, previous methods either constrain the median or avoid constraints. In this article, we propose a centered stick-breaking process (CSBP), which induces mean and variance constraints on an unknown distribution in a hierarchical model. This is accomplished by viewing an unconstrained stick-breaking process as a parameter-expanded version of a CSBP. An efficient blocked Gibbs sampler is developed for approximate posterior computation. The methods are illustrated through a simulated example and an epidemiologic application.
authors.affiliation: School of Public Health, Saint Louis University, United States.
authors.forename: Mingan
authors.initials: M
authors.lastname: Yang
authors.affiliation: Department of Statistical Science, Duke University, United States.
authors.forename: David B
authors.initials: DB
authors.lastname: Dunson
authors.affiliation: Epidemiology Branch, National Institute of Environmental Health Sciences, Research Triangle Park, NC 27709, United States.
authors.forename: Donna
authors.initials: D
authors.lastname: Baird
keywords: Dirichlet process; Latent variables; Moment constraints; Nonparametric Bayes; Parameter expansion; Random effects