Bayesian regression trees are flexible non-parametric models that are well
suited to many modern statistical regression problems. Many such tree models
have been proposed, from the simple single- tree model to more complex tree
ensembles. Their non-parametric formulation allows for effective and efficient
modeling of datasets exhibiting complex non-linear relationships between the
model pre- dictors and observations. However, the mixing behavior of the Markov
Chain Monte Carlo (MCMC) sampler is sometimes poor. This is because the
proposals in the sampler are typically local alterations of the tree structure,
such as the birth/death of leaf nodes, which does not allow for efficient
traversal of the model space. This poor mixing can lead to inferential
problems, such as under-representing uncertainty. In this paper, we develop
novel proposal mechanisms for efficient sampling. The first is a rule
perturbation proposal while the second we call tree rotation. The perturbation
proposal can be seen as an efficient variation of the change proposal found in
existing literature. The novel tree rotation proposal is simple to implement as
it only requires local changes to the regression tree structure, yet it
efficiently traverses disparate regions of the model space along contours of
equal probability. When combined with the classical birth/death proposal, the
resulting MCMC sampler exhibits good acceptance rates and properly represents
model uncertainty in the posterior samples. We implement this sampling
algorithm in the Bayesian Additive Regression Tree (BART) model and demonstrate
its effectiveness on a prediction problem from computer experiments and a test
function where structural tree variability is needed to fully explore the
posterior.

本文提出了一种针对贝叶斯回归树的采样算法，其中包括规则扰动和树旋转等提议机制，这些机制在与传统的出生 / 死亡提议相结合时，可以提高 MCMC 采样器的接受率，并在后验样本中合理表示模型不确定性。