Bayesian Additive Regression Trees with Basis-Expanded Functional Covariates

In the fields of environmental science and medicine it is increasingly common to have access to data collected on subjects over time. Given a sufficiently dense sampling, these data can often be smoothed and analyzed as functional variables. While functional variables can be used as covariates in regression models, traditional methods, such as the functional linear model, impose constraints that limit the usefulness of functional covariates as predictors. In this paper we introduce Basis-Expanded Bayesian Additive Regression Trees (BBART), an adaptation to the original BART model that allows for the inclusion of functional covariates. By leveraging the BART model, BBART inherits many attractive features, including requiring no assumption of additivity or smooth effects and enabling posterior inference with MCMC samples.