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Modeling Covariates with Nonparametric Bayesian Methods

28 Pages Posted: 26 Mar 2010  

Alejandro Cruz-Marcelo

Capital One Auto Finance

Gary R. Rosner

University of Texas at Houston - M.D. Anderson Cancer Center

Peter Mueller

The University of Texas M. D. Anderson Cancer Center

Clinton Stewart

affiliation not provided to SSRN

Date Written: March 22, 2010

Abstract

A research problem that has received increased attention in recent years is extending Bayesian nonparametric methods to include dependence on covariates. Limited attention, however, has been directed to the following two aspects. First, analyzing how the performance of such extensions differs, and second, understanding which features are worthwhile in order to produce better results. This article proposes answers to those questions focusing on predictive inference and continuous covariates. Specifically, we show that 1) nonparametric models using different strategies for modeling continuous covariates can show noteworthy differences when they are being used for prediction, even though they produce otherwise similar posterior inference results, and 2) when the predictive density is a mixture, it is convenient to make the weights depend on the covariates in order to produce sensible estimators. Such claims are supported by comparing the Linear DDP (an extension of the Sethuraman representation) and the Conditional DP (which augments the nonparametric distribution to include the covariates). Unlike the Conditional DP, the weights in the predictive mixture density of the Linear DDP are not covariate-dependent. This results in poor estimators of the predictive density. Specifically, in a simulation example, the Linear DDP wrongly introduces an additional mode into the predictive density, while in an application to a pharmacokinetic study, it produces unrealistic concentration-time curves.

Keywords: Dirichlet process mixture, Hierarchical model, Nonparametric Bayes, Covariates modeling, Dependent Dirichlet process

Suggested Citation

Cruz-Marcelo, Alejandro and Rosner, Gary R. and Mueller, Peter and Stewart, Clinton, Modeling Covariates with Nonparametric Bayesian Methods (March 22, 2010). Available at SSRN: https://ssrn.com/abstract=1576665 or http://dx.doi.org/10.2139/ssrn.1576665

Alejandro Cruz-Marcelo (Contact Author)

Capital One Auto Finance ( email )

7933 Preston Road
Plano, TX 75093
United States

Gary R. Rosner

University of Texas at Houston - M.D. Anderson Cancer Center ( email )

1515 Holocombe Blvd
Houston, TX 77030
United States

Peter Mueller

The University of Texas M. D. Anderson Cancer Center ( email )

Houston, TX 77030
United States

Clinton Stewart

affiliation not provided to SSRN ( email )

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