Bayesian Additive Regression Trees for Multivariate Skewed Responses

• Activity Number: 171 - SPAAC Poster Competition
• Type: Topic Contributed
• Date/Time: Tuesday, August 4, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Seungha Um* and Antonio Linero and Debajyoti Sinha and Dipankar Bandyopadhyay
• Companies: Florida State University and University of Texas at Austin and Florida State University and Virginia Commonwealth University
• Keywords: Bayesian additive regression trees; Ensemble method; Multivariate responses; Nonlinear regression; Skew-normal density

Abstract

This paper introduces a nonparametric regression approach for univariate and multivariate skewed responses using Bayesian additive regression trees (BART). Existing BART using ensembles of decision trees to model a mean function has become highly popular recently due to its high prediction accuracy and ease of use. Instead of usual BART with a typical univariate Gaussian error distribution assumption that is restrictive in many biomedical applications, we provide a useful extension of the BART, called skewBART model, for skewed responses of our motivating oral health study. We also extend skewBART for univariate response to multivariate responses and even allow sharing of information across decision trees associated with different responses within same subject. The methodology also accommodates the within subject association as well as different skewness parameters for different multivariate responses. We illustrate the benet of our multivariate skewBART model by analyzing the oral health study with highly skewed multiple responses.