Math @ Duke

Publications [#257925] of David B. Dunson
search www.stat.duke.edu.Papers Published
 Neelon, B; Dunson, DB, Bayesian isotonic regression and trend analysis,
Biometrics, vol. 60 no. 2
(2004),
pp. 398406 [doi]
(last updated on 2017/12/17)
Abstract: In many applications, the mean of a response variable can be assumed to be a nondecreasing function of a continuous predictor, controlling for covariates. In such cases, interest often focuses on estimating the regression function, while also assessing evidence of an association. This article proposes a new framework for Bayesian isotonic regression and orderrestricted inference. Approximating the regression function with a highdimensional piecewise linear model, the nondecreasing constraint is incorporated through a prior distribution for the slopes consisting of a product mixture of point masses (accounting for flat regions) and truncated normal densities. To borrow information across the intervals and smooth the curve, the prior is formulated as a latent autoregressive normal process. This structure facilitates efficient posterior computation, since the full conditional distributions of the parameters have simple conjugate forms. Point and interval estimates of the regression function and posterior probabilities of an association for different regions of the predictor can be estimated from a single MCMC run. Generalizations to categorical outcomes and multiple predictors are described, and the approach is applied to an epidemiology application.


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