Assessing variable activity for Bayesian regression trees

Bayesian Additive Regression Trees (BART) are non-parametric models that can capture complex exogenous variable effects. In any regression problem, it is often of interest to learn which variables most active. Variable activity in BART usually measured by counting the number times a tree splits for each variable. Such one-way counts have advantage fast computations. Despite their convenience, several issues. They statistically unjustified, cannot distinguish between main effects and interaction effects, become inflated when measuring An alternative method well-established literature Sobo? indices, variance-based global sensitivity analysis technique. However, these indices require Monte Carlo integration, be computationally expensive. This paper provides analytic expressions posterior samples. These easy interpret feasible. Furthermore, we will show fascinating connection first-order (main-effects) counts. We also introduce novel ranking method, use this demonstrate proposed preserve Sobo?-based rank order importance. Finally, compare methods using test functions En-ROADS climate impacts simulator.