Bayesian semiparametric isotonic regression for count data

Published

Journal Article

This article proposes a semiparametric Bayesian approach for inference on an unknown isotonic regression function, f(x), characterizing the relationship between a continuous predictor, X, and a count response variable, Y, adjusting for covariates, Z. A Dirichlet process mixture of Poisson distributions is used to avoid parametric assumptions on the conditional distribution of Y given X and Z. Then, to also avoid parametric assumptions on f(x), a novel prior formulation is proposed that enforces the nondecreasing constraint and assigns positive prior probability to the null hypothesis of no association. Through the use of carefully tailored hyperprior distributions, we allow for borrowing of information across different regions of X in estimating f(x) and in assessing hypotheses about local increases in the function. Due to conjugacy properties, posterior computation is straightforward using a Markov chain Monte Carlo algorithm. The methods are illustrated using data from an epidemiologic study of sleep problems and obesity.

Full Text

Duke Authors

Cited Authors

  • Dunson, DB

Published Date

  • June 1, 2005

Published In

Volume / Issue

  • 100 / 470

Start / End Page

  • 618 - 627

International Standard Serial Number (ISSN)

  • 0162-1459

Digital Object Identifier (DOI)

  • 10.1198/016214504000001457

Citation Source

  • Scopus