B1802
Title: spBART: Adding smoothness for Bayesian additive regression trees through splines
Authors: Mateus Maia Marques - Maynooth University (Ireland) [presenting]
Abstract: In recent years, Bayesian additive regression trees (BART) have risen to prominence as a versatile tool for nonparametric regression analysis, finding utility in diverse domains such as economics, finance, and medicine. However, a notable constraint inherent to the original BART model is its assumption of piecewise constant smoothness, a limitation that can prove detrimental when confronting scenarios where a continuous, smooth underlying function is presumed. The purpose is to address this limitation by introducing an extension to the BART model that incorporates splines within terminal nodes. This extension is referred to as "Splines Bayesian Additive Regression Trees" (sBART). The Bayesian approach is presented for the choice of model priors distributions, its hyperparameters and the Markov chain Monte Carlo sampler to obtain the posterior samples from the model. The method, sBART, stands as a robust and flexible instrument for nonparametric regression analysis, offering the attribute of accommodating smoothness in the underlying function jointly with the consolidated good performance of BART on statistical modelling. This advancement represents a noteworthy contribution to the field of nonparametric regression, facilitating more accurate and adaptable modeling in scenarios where smoothness is of paramount importance. Various simulated and real examples are shown as evidence of the potential of sBART.
