mBART: Multidimensional Monotone BART

For the discovery of regression relationships between Y and a large set p potential predictors x1,…,xp, flexible nonparametric nature BART (Bayesian Additive Regression Trees) allows for much richer possibilities than restrictive parametric approaches. However, subject matter considerations sometimes warrant minimal assumption monotonicity in at least some predictors. such contexts, we introduce mBART, constrained version that can flexibly incorporate any predesignated subset using multivariate basis monotone trees, while avoiding further confines full form. relationships, mBART provides (i) function estimates are smoother more interpretable, (ii) better out-of-sample predictive performance, (iii) less post-data uncertainty. While many key aspects unconstrained model carry over directly to introduction constraints necessitates fundamental rethinking how is implemented. In particular, original Markov Chain Monte Carlo algorithm relied on conditional conjugacy no longer available monotonically space. Various simulated real examples demonstrate wide ranging mBART.