MCMC diagnostics for Bayesian additive regression trees and methods for flexible modeling of predictors

Bayesian Additive Regression Trees (BART) is a relatively new model within the domain of statistical/machine learning. BART has seen rapid development in recent years, having been extended and adapted to new application areas. Given that BART is a fully Bayesian model, care should be taken to justify that samples drawn via Markov Chain Monte Carlo (MCMC) from BART’s posterior distribution can be regarded as from a stationary posterior distribution. Presently, no formal method exists for conducting such diagnostic checks. As such, a formal convergence criterion is developed for BART called the Posterior Tree Deviance (PTD). This method for assessing convergence of BART’s MCMC sampler is implemented in a novel software package, BART.jl, written in the Julia programming language. Working with BART presents an onerous software burden. BART.jl contains a much smaller codebase than implementations in other programming languages and provides user-friendly functionality for working with BART’s ensemble of decision trees. Lastly, BART is adapted to two novel application areas: (1) variable selection in the presence of mandatory and optional covariates (2) correcting for bias resulting from a predictor measured with error.