Dirichlet-Tree Allocation Priors for Bayesian Causal Forests

Bayesian Causal Forests (BCF) estimate heterogeneous treatment effects with a separate ensemble of treatment trees. The prior on the leaf values of the treatment trees determines whether sampling variability is attributed to the treatment effect. Independent shrinkage priors exert no control over how a tree allocates variability across its leaves, and their total prior variance grows as leaves are added. We propose the Dirichlet-Tree Bayesian Causal Forest, which jointly regularizes the leaf values of each treatment tree through a Dirichlet-Tree prior on their variance shares, generated by stick-breaking along the tree topology. We characterize the spike and tails of the marginal leaf prior, show that the prior adaptively bounds the number of regions of effect heterogeneity, and establish posterior consistency for the forest. In simulations, the model outperforms BCF when heterogeneity is confined to a few regions and reduces spurious heterogeneity elsewhere, and, unlike independent shrinkage priors, its accuracy does not deteriorate as the trees grow. We also evaluate the model on real data, including a pancreatic cancer survival study.