Effect on prediction when modeling covariates in Bayesian nonparametric models

Alejandro Cruz-Marcelo, Gary Rosner, Peter Müller, Clinton F. Stewart

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)204-218
Number of pages15
JournalJournal of Statistical Theory and Practice
Volume7
Issue number2
DOIs
StatePublished - Jan 1 2013

Fingerprint

Bayesian Nonparametrics
Nonparametric Model
Bayesian Model
Covariates
Prediction
Modeling
Random Probability Measure
Predictive Density
Oncology
Pediatrics
Bayesian Methods
Bayesian inference
Parametric Model
Dose
Drugs
Demonstrate
Observation

Keywords

  • Covariates modeling
  • Dependent Dirichlet process
  • Dirichlet process mixture
  • Hierarchical model
  • Nonparametric Bayes
  • Predictive distribution

ASJC Scopus subject areas

  • Statistics and Probability

Cite this

Effect on prediction when modeling covariates in Bayesian nonparametric models. / Cruz-Marcelo, Alejandro; Rosner, Gary; Müller, Peter; Stewart, Clinton F.

In: Journal of Statistical Theory and Practice, Vol. 7, No. 2, 01.01.2013, p. 204-218.

Research output: Contribution to journalArticle

Cruz-Marcelo, Alejandro ; Rosner, Gary ; Müller, Peter ; Stewart, Clinton F. / Effect on prediction when modeling covariates in Bayesian nonparametric models. In: Journal of Statistical Theory and Practice. 2013 ; Vol. 7, No. 2. pp. 204-218.
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