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Abstract:
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Bayesian Additive Regression Trees (BART) has recently seen rapid development. Often used in pure prediction problems, a major advantage of BART is its seamless uncertainty quantification via its posterior distribution. Since BART is a fully Bayesian model, care should be taken to check whether samples drawn from its posterior have sufficiently mixed and are representative of an underlying stationary distribution. The marginal likelihood for BART is derived, allowing for the computation of the marginal posterior distribution of the decision tree ensemble employed in BART. We propose -2 times the log of this marginal posterior as a formal convergence diagnostic for BART’s decision tree ensemble, which we refer to as the Posterior Tree Deviance (PTD). It is also shown that this diagnostic is available for probit BART. Simulation studies are presented that demonstrate scenarios in which convergence based solely on the error variance erroneously conclude the chains to have mixed and converged, resulting in a detrimental impact on prediction intervals. However, convergence based on the PTD correctly diagnoses these convergence issues with the decision tree ensemble.
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