Accelerating BART: A Sequential Non-Parametric Framework for Real-Time MCMC Convergence

Bayesian Additive Regression Trees is a powerful non-parametric model for learning complex nonlinear relationships, but its reliability depends on the convergence of the underlying Markov Chain Monte Carlo sampler. Standard diagnostics with effective sample size are typically applied post-hoc, requiring a burn-in specification and often multiple chains. Consequently, sampling may continue long after convergence, leading to unnecessary computational cost. We propose a real-time convergence framework that integrates the exact non-parametric sequential convergence test into the bartMachine environment. The method, an alpha-spending strategy, sequentially evaluates the distributional stability of Hastings acceptance ratios during Metropolis-in-Gibbs updates, providing a statistically grounded stopping rule that operates during sampling and controls false positives, eliminating the need for predetermined iteration counts. Extensive simulations with diverse sample sizes, noise levels, and signal strengths demonstrate perfect convergence detection across all scenarios and show that monitoring acceptance-ratio stabilization provides an efficient and principled mechanism to accelerate BART inference with convergence control, yielding substantial computational gains preserving inferential accuracy.