Exploiting independence for branch operations in Bayesian learning of C&RTs

In this paper we extend a methodology for Bayesian learning via MCMC, with the ability to grow arbitrarily long branches in C&RT models. We are able to do so by exploiting independence in the model construction process. The ability to grow branches rather than single nodes has been noted as desirable in the literature. The most singular feature of the underline methodology used here in comparison to other approaches is the coupling of the prior and the proposal. The main contribution of this paper is to show how taking advantage of independence in the coupled process, can allow branch growing and swapping for proposal models.