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Bayesian nonparametric estimation of continuous monotone functions with applications to dose-response analysis.

Research paper by Björn B Bornkamp, Katja K Ickstadt

Indexed on: 31 May '08Published on: 31 May '08Published in: Biometrics



Abstract

In this article, we consider monotone nonparametric regression in a Bayesian framework. The monotone function is modeled as a mixture of shifted and scaled parametric probability distribution functions, and a general random probability measure is assumed as the prior for the mixing distribution. We investigate the choice of the underlying parametric distribution function and find that the two-sided power distribution function is well suited both from a computational and mathematical point of view. The model is motivated by traditional nonlinear models for dose-response analysis, and provides possibilities to elicitate informative prior distributions on different aspects of the curve. The method is compared with other recent approaches to monotone nonparametric regression in a simulation study and is illustrated on a data set from dose-response analysis.