Bayesian inferences on umbrella orderings.

Published

Journal Article

In regression applications with categorical predictors, interest often focuses on comparing the null hypothesis of homogeneity to an ordered alternative. This article proposes a Bayesian approach for addressing this problem in the setting of normal linear and probit regression models. The regression coefficients are assigned a conditionally conjugate prior density consisting of mixtures of point masses at 0 and truncated normal densities, with a (possibly unknown) changepoint parameter included to accommodate umbrella ordering. Two strategies of prior elicitation are considered: (1) a Bayesian Bonferroni approach in which the probability of the global null hypothesis is specified and local hypotheses are considered independent; and (2) an approach which treats these probabilities as random. A single Gibbs sampling chain can be used to obtain posterior probabilities for the different hypotheses and to estimate regression coefficients and predictive quantities either by model averaging or under the preferred hypothesis. The methods are applied to data from a carcinogenesis study.

Full Text

Duke Authors

Cited Authors

  • Hans, C; Dunson, DB

Published Date

  • December 2005

Published In

Volume / Issue

  • 61 / 4

Start / End Page

  • 1018 - 1026

PubMed ID

  • 16401275

Pubmed Central ID

  • 16401275

Electronic International Standard Serial Number (EISSN)

  • 1541-0420

International Standard Serial Number (ISSN)

  • 0006-341X

Digital Object Identifier (DOI)

  • 10.1111/j.1541-0420.2005.00373.x

Language

  • eng