Bayesian regression structure discovery
Hugh Chipman, Edward I. George, Robert E. McCulloch · Oxford University Press eBooks · 2013
This chapter describes two different Bayesian approaches that illustrate the vast potential of Bayesian methods to extract information hidden in high-dimensional data. The first is based on the classical parametric form of the normal linear model, while the second is based on an approach called BART (Bayesian Additive Regression Trees). It shows that although the overall BART sum-of-trees model is complex, the simple structure of the individual tree components enables us to uncover structure with inferential posterior summaries. In particular, it is shown how BART provides a novel approach to model-free variable selection, the search for interesting variables, and model-free interaction detection and the search for interesting pairs of variables.