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Activity Number: 500 - Statistical Learning
Type: Contributed
Date/Time: Thursday, August 6, 2020 : 10:00 AM to 2:00 PM
Sponsor: Section on Statistical Learning and Data Science
Abstract #313202
Title: Inference for BART with Multinomial Outcomes
Author(s): Yizhen Xu* and Rami Kantor and Ann Mwangi and Michael Daniels and Joseph Hogan
Companies: Brown University and Brown University and Moi University and University of Florida and Brown University
Keywords: Parameter expansion; Latent variable model; BART; Multinomial probit

The multinomial probit Bayesian additive regression trees (MPBART) framework was proposed by Kindo et al. (2016) to approximate the latent utilities in multinomial probit (MNP) model with Bayesian additive regression trees (BART). Compared to multinomial logistic models, MNP does not assume independent alternatives and naturally obtain a Bayesian estimation of the correlation structure among alternatives through the multivariate Gaussian distributed latent utilities. We introduce two algorithms for fitting the MPBART and show that the theoretical mixing rates of our proposals are at least as good as the existing algorithm (KD) proposed by Kindo et al. We also discuss the robustness of the methods to the choice of reference level, the imbalance in outcome frequencies, and the specifications of prior hyperparameters for the utility error term. Through simulations and application, we observe improvement in our proposals compared to KD in terms of MCMC convergence rate and posterior predictive accuracy.

Authors who are presenting talks have a * after their name.

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