Bayesian semiparametric isotonic regression for count data

doi:10.1198/016214504000001457

Bayesian semiparametric isotonic regression for count data

2005-06-01

54

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AI

D

Dunson, DB *

DOI：10.1198/016214504000001457

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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.

Keyword:

Dirichlet process mixture

generalized additive model

log linear

mixture prior

multiple testing

nonparametric regression

smoothing

variable selection

Bayesian semiparametric isotonic regression for count data

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