Uncertainty quantification for Bayesian CART

This work affords new insights into Bayesian CART in the context of structured wavelet shrinkage. The main thrust is to develop a formal inferential framework for tree-based regression. We reframe as g-type prior which departs from typical product priors by harnessing correlation induced tree topology. practically used are shown attain adaptive near rate-minimax posterior concentration supremum norm regression models. For fundamental goal uncertainty quantification, we construct confidence bands function with uniform coverage under self-similarity. In addition, show that tree-posteriors enable optimal inference form efficient sets smooth functionals function.