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Bayesian semiparametric isotonic regression for count data

Publication ,  Journal Article
Dunson, DB
Published in: Journal of the American Statistical Association
June 1, 2005

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.

Duke Scholars

Published In

Journal of the American Statistical Association

DOI

ISSN

0162-1459

Publication Date

June 1, 2005

Volume

100

Issue

470

Start / End Page

618 / 627

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1603 Demography
  • 1403 Econometrics
  • 0104 Statistics
 

Citation

APA
Chicago
ICMJE
MLA
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Dunson, D. B. (2005). Bayesian semiparametric isotonic regression for count data. Journal of the American Statistical Association, 100(470), 618–627. https://doi.org/10.1198/016214504000001457
Dunson, D. B. “Bayesian semiparametric isotonic regression for count data.” Journal of the American Statistical Association 100, no. 470 (June 1, 2005): 618–27. https://doi.org/10.1198/016214504000001457.
Dunson DB. Bayesian semiparametric isotonic regression for count data. Journal of the American Statistical Association. 2005 Jun 1;100(470):618–27.
Dunson, D. B. “Bayesian semiparametric isotonic regression for count data.” Journal of the American Statistical Association, vol. 100, no. 470, June 2005, pp. 618–27. Scopus, doi:10.1198/016214504000001457.
Dunson DB. Bayesian semiparametric isotonic regression for count data. Journal of the American Statistical Association. 2005 Jun 1;100(470):618–627.
Journal cover image

Published In

Journal of the American Statistical Association

DOI

ISSN

0162-1459

Publication Date

June 1, 2005

Volume

100

Issue

470

Start / End Page

618 / 627

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1603 Demography
  • 1403 Econometrics
  • 0104 Statistics