Objective selection of the number of trees in BART for conditional copula models

Determine an objective, data-driven procedure for selecting the total number of trees m in Bayesian Additive Regression Trees (BART) when estimating conditional copula parameters, so that modelers need not rely on ad hoc defaults or manual tuning across multiple fitted models.

Background

In the proposed conditional copula framework, the copula parameter is modeled via a sum-of-trees BART representation with a loss-based prior on tree topology. While BART flexibly captures complex functional relationships, its performance and computational cost depend critically on the chosen number of trees m.

The literature commonly adopts fixed defaults (e.g., 200 or 500 trees), and in this work the authors monitor performance by starting with 5 trees and increasing by 5. This empirical strategy is computationally expensive and lacks principled guidance, motivating the explicit identification of the need for an objective method to select m.