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Activity Number:
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33
- Junior Research in Methods for Integrating Heterogeneous Data: From Clustering to Factor Analysis
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Type:
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Topic Contributed
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Date/Time:
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Monday, August 3, 2020 : 10:00 AM to 11:50 AM
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Sponsor:
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International Society for Bayesian Analysis (ISBA)
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Abstract #309698
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Title:
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VC-BART: Bayesian Trees for Varying Coefficients
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Author(s):
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Sameer Deshpande* and Ray Bai and Cecilia Balocchi and Jennifer E Starling
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Companies:
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CSAIL, MIT and University of Pennsylvania and University of Pennsylvania and The University of Texas at Austin
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Keywords:
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Semiparametric regression;
MCMC;
Treed Regression;
Longitudinal Studies
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Abstract:
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The linear varying coefficient model generalizes the conventional linear model by allowing the additive effect of each covariate X on the outcome Y to vary as a function of additional effect modifiers Z. While there are many existing procedures for fitting such a model when the effect modifier Z is a scalar (typically time), there has been comparatively less development for settings with multivariate Z. In this work, we present an extension of Bayesian Additive Regression Trees (BART) to the varying coefficient model for applications in which we might reasonable suspect covariate effects vary systematically with respect to interactions between multiple modifiers. We derive a straightforward Gibbs sampler based on the familiar "Bayesian backfitting" procedure of Chipman, George, and McCulloch (2010) that also allows for correlated residual errors. We further build on recent theoretical advances for the varying-coefficient model and BART to derive posterior concentration rates under our model. We demonstrate our method on several econometric and spatiotemporal examples.
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Authors who are presenting talks have a * after their name.
