Abstract
For the discovery of regression relationships between Y and a large set of p potential predictors x 1,…, xp, the flexible nonparametric nature of BART (Bayesian Additive Regression Trees) allows for a much richer set of possibilities than restrictive parametric approaches. However, subject matter considerations sometimes warrant a minimal assumption of monotonicity in at least some of the predictors. For such contexts, we introduce mBART, a constrained version of BART that can flexibly incorporate monotonicity in any predesignated subset of predictors using a multivariate basis of monotone trees, while avoiding the further confines of a full parametric form. For such monotone relationships, mBART provides (i) function estimates that are smoother and more interpretable, (ii) better out-of-sample predictive performance, and (iii) less post-data uncertainty. While many key aspects of the unconstrained BART model carry over directly to mBART, the introduction of monotonicity constraints necessitates a fundamental rethinking of how the model is implemented. In particular, the original BART Markov Chain Monte Carlo algorithm relied on a conditional conjugacy that is no longer available in a monotonically constrained space. Various simulated and real examples demonstrate the wide ranging potential of mBART.
Original language | English (US) |
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Pages (from-to) | 515-544 |
Number of pages | 30 |
Journal | Bayesian Analysis |
Volume | 17 |
Issue number | 2 |
DOIs | |
State | Published - Jun 2022 |
Keywords
- Bayesian nonparametrics
- MCMC algorithm
- ensemble model
- isotonic regression
- multidimensional nonparametric regression
- shape constrained inference
ASJC Scopus subject areas
- Statistics and Probability
- Applied Mathematics