  In recent years, Bayesian Additive Regression Trees (BART) has garnered
increased attention, leading to the development of various extensions for
diverse applications. However, there has been limited exploration of its
utility in analyzing correlated data. This paper introduces a novel extension
of BART, named Correlated BART (CBART). Unlike the original BART with
independent errors, CBART is specifically designed to handle correlated
(dependent) errors. Additionally, we propose the integration of CBART with
Gaussian processes (GP) to create a new model termed GP-CBART. This innovative
model combines the strengths of the Gaussian processes and CBART, making it
particularly well-suited for analyzing time series or spatial data. In the
GP-CBART framework, CBART captures the nonlinearity in the mean regression
(covariates) function, while the Gaussian processes adeptly models the
correlation structure within the response. Additionally, given the high
flexibility of both CBART and GP models, their combination may lead to
identification issues. We provide methods to address these challenges. To
demonstrate the effectiveness of CBART and GP-CBART, we present corresponding
simulated and real-world examples.
