Fully Nonparametric Bayesian Additive Regression Trees
Robert McCulloch and
A chapter in Topics in Identification, Limited Dependent Variables, Partial Observability, Experimentation, and Flexible Modeling: Part B, 2019, vol. 40B, pp 89-110 from Emerald Publishing Ltd
Abstract Bayesian additive regression trees (BART) is a fully Bayesian approach to modeling with ensembles of trees. BART can uncover complex regression functions with high-dimensional regressors in a fairly automatic way and provide Bayesian quantification of the uncertainty through the posterior. However, BART assumes independent and identical distributed (i.i.d) normal errors. This strong parametric assumption can lead to misleading inference and uncertainty quantification. In this chapter we use the classic Dirichlet process mixture (DPM) mechanism to nonparametrically model the error distribution. A key strength of BART is that default prior settings work reasonably well in a variety of problems. The challenge in extending BART is to choose the parameters of the DPM so that the strengths of the standard BART approach is not lost when the errors are close to normal, but the DPM has the ability to adapt to non-normal errors.
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