Bayesian nonparametric estimation of continuous monotone functions with applications to dose-response analysis.
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.
Bornkamp
Björn
B
Fakultät Statistik, Technische Universität Dortmund, 44221 Dortmund, Germany. bornkamp@statistik.tu-dortmund.de
Ickstadt
Katja
K
D001499:Bayes Theorem; D001699:Biometry / Q000379:methods*; D003627:Data Interpretation, Statistical; D004305:Dose-Response Relationship, Drug; D006801:Humans; D008962:Models, Theoretical; D018709:Statistics, Nonparametric