Effect on Prediction When Modeling Covariates in Bayesian Nonparametric Models
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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.
KeywordsCovariates modeling Dependent Dirichlet process Dirichlet process mixture Hierarchical model Nonparametric Bayes Predictive distribution
AMS Subject Classification62G05
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- Cifarelli, D., and E. Regazzini, 1978. Nonparametric statistical problems under partial exchangeability. the use of associative means. Ann. Inst. Mat. Finianz. Univ. Torino, 12, 1–36.Google Scholar
- Gibaldi, M., and D. Perrier. 1982. Pharmacokinetics, 2nd ed. New York, NY, Marcel Dekker.Google Scholar
- MacEachern, S. 1999. Dependent nonparametric processes. In ASA Proceedings of the Section on Bayesian Statistical Science, 50–55. Alexandria, VA, American Statistical Association.Google Scholar
- MacEachern, S., and P. Müller. 1998. Estimating mixture of Dirichlet process models. J. Comput. Graph. Stat., 7(2), 223–238.Google Scholar