  We present a novel prior for tree topology within Bayesian Additive
Regression Trees (BART) models. This approach quantifies the hypothetical loss
in information and the loss due to complexity associated with choosing the
wrong tree structure. The resulting prior distribution is compellingly geared
toward sparsity, a critical feature considering BART models' tendency to
overfit. Our method incorporates prior knowledge into the distribution via two
parameters that govern the tree's depth and balance between its left and right
branches. Additionally, we propose a default calibration for these parameters,
offering an objective version of the prior. We demonstrate our method's
efficacy on both simulated and real datasets.
