Bayesian nonparametric estimation of continuous monotone functions with applications to dose-response analysis. (English) Zbl 1159.62023
Summary: 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.
MSC:
| 62G08 | Nonparametric regression and quantile regression |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 62F15 | Bayesian inference |
Keywords:
Bayesian nonparametric regression; dose estimation; monotone regression; reversible jump MCMCSoftware:
bnpmrReferences:
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