A Formal MCMC Convergence Diagnostic for  Bayesian

Additive Regression Trees

Brandon Butcher Ph.D. Candidate

Department of Biostatistics University of Iowa

Iowa City, IA

Colloquium Talk University of New Mexico

Department of Mathematics & Statistics March 3, 2020

 

Bayesian Additive Regression Trees (BART) (Chipman, George, & McCulloch; 2010) has seen rapid development in recent years. An open research question that has yet to be formally ad-  dressed is how to diagnose convergence of the MCMC sampler that has been developed for BART.  In this talk, 

I’ll present work from from my dissertation where I provide a formal solution to this open question.  This solution is based on the derivation of BART’s marginal likelihood, allowing for the direct computation of the posterior distribution of the decision tree ensembles on which BART is based.  It is proposed that convergence of BART be monitored using -2 times the log of the posterior distribution of the decision tree ensembles, which we refer to as the Posterior Tree Deviance (PTD). The utility of our diagnostic is demonstrated using a simulation study set-up in which BART’s MCMC sampler is known to suffer from issues with mixing. An application to predicting risk for ischemic stroke is also presented.