Bayesian Survival Tree Ensembles with Submodel Shrinkage

We consider Bayesian nonparametric estimation of a survival time subject to right-censoring in the presence potentially high-dimensional predictors. argue that several approaches, such as random forests and existing possess drawbacks, including: computational difficulties; lack known theoretical properties; ineffectiveness at filtering out irrelevant propose two models based on additive regression trees (BART) framework. The first, Modulated BART (MBART), is fully-nonparametric failure first occurrence non-homogeneous Poisson process. second, CoxBART, uses implementation Cox’s partial likelihood. These are adapted predictors, have default prior specifications, require simple modifications methods implement. show effectiveness these simulated benchmark datasets. also establish that, for simplified variant MBART, posterior distribution contracts near-minimax optimal rate sparse asymptotic regime.