TY - JOUR
T1 - Effect on prediction when modeling covariates in Bayesian nonparametric models
AU - Cruz-Marcelo, Alejandro
AU - Rosner, Gary L.
AU - Müller, Peter
AU - Stewart, Clinton F.
N1 - Funding Information:
This research was supported by the National Cancer Institute grant R01CA075981; the Brown Foundation Fellowship, Center for Computational Finance and Economic Systems; and the NSF VIGRE grant DSM-0739420.
PY - 2013/1/1
Y1 - 2013/1/1
N2 - In biomedical research, it is often of interest to characterize biologic processes giving rise to observations and to make predictions of future observations. Bayesian nonparamric methods provide a means for carrying out Bayesian inference making as few assumptions about restrictive parametric models as possible. There are several proposals in the literature for extending Bayesian nonparametric models to include dependence on covariates. In this article, we examine the effect on fitting and predictive performance of incorporating covariates in a class of Bayesian nonparametric models by one of two primary ways: either in the weights or in the locations of a discrete random probability measure. We show that different strategies for incorporating continuous covariates in Bayesian nonparametric models can result in big differences when used for prediction, even though they lead to otherwise similar posterior inferences. When one needs the predictive density, as in optimal design, and this density is a mixture, it is better to make the weights depend on the covariates. We demonstrate these points via a simulated data example and in an application in which one wants to determine the optimal dose of an anticancer drug used in pediatric oncology.
AB - In biomedical research, it is often of interest to characterize biologic processes giving rise to observations and to make predictions of future observations. Bayesian nonparamric methods provide a means for carrying out Bayesian inference making as few assumptions about restrictive parametric models as possible. There are several proposals in the literature for extending Bayesian nonparametric models to include dependence on covariates. In this article, we examine the effect on fitting and predictive performance of incorporating covariates in a class of Bayesian nonparametric models by one of two primary ways: either in the weights or in the locations of a discrete random probability measure. We show that different strategies for incorporating continuous covariates in Bayesian nonparametric models can result in big differences when used for prediction, even though they lead to otherwise similar posterior inferences. When one needs the predictive density, as in optimal design, and this density is a mixture, it is better to make the weights depend on the covariates. We demonstrate these points via a simulated data example and in an application in which one wants to determine the optimal dose of an anticancer drug used in pediatric oncology.
KW - Covariates modeling
KW - Dependent Dirichlet process
KW - Dirichlet process mixture
KW - Hierarchical model
KW - Nonparametric Bayes
KW - Predictive distribution
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U2 - 10.1080/15598608.2013.772811
DO - 10.1080/15598608.2013.772811
M3 - Article
C2 - 23687472
AN - SCOPUS:84876110434
SN - 1559-8608
VL - 7
SP - 204
EP - 218
JO - Journal of Statistical Theory and Practice
JF - Journal of Statistical Theory and Practice
IS - 2
ER -