Bayesian isotonic density regression.

Published

Journal Article

Density regression models allow the conditional distribution of the response given predictors to change flexibly over the predictor space. Such models are much more flexible than nonparametric mean regression models with nonparametric residual distributions, and are well supported in many applications. A rich variety of Bayesian methods have been proposed for density regression, but it is not clear whether such priors have full support so that any true data-generating model can be accurately approximated. This article develops a new class of density regression models that incorporate stochastic-ordering constraints which are natural when a response tends to increase or decrease monotonely with a predictor. Theory is developed showing large support. Methods are developed for hypothesis testing, with posterior computation relying on a simple Gibbs sampler. Frequentist properties are illustrated in a simulation study, and an epidemiology application is considered.

Full Text

Duke Authors

Cited Authors

  • Wang, L; Dunson, DB

Published Date

  • September 2011

Published In

Volume / Issue

  • 98 / 3

Start / End Page

  • 537 - 551

PubMed ID

  • 22822259

Pubmed Central ID

  • 22822259

Electronic International Standard Serial Number (EISSN)

  • 1464-3510

International Standard Serial Number (ISSN)

  • 0006-3444

Digital Object Identifier (DOI)

  • 10.1093/biomet/asr025

Language

  • eng