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Bayesian Theory and Applications$
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Paul Damien, Petros Dellaportas, Nicholas G. Polson, and David A. Stephens

Print publication date: 2013

Print ISBN-13: 9780199695607

Published to Oxford Scholarship Online: May 2013

DOI: 10.1093/acprof:oso/9780199695607.001.0001

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Bayesian regression structure discovery

Bayesian regression structure discovery

Chapter:
(p.451) 22 Bayesian regression structure discovery
Source:
Bayesian Theory and Applications
Author(s):

Hugh A. Chipman

Edward I George

Robert E. McCulloch

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199695607.003.0022

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.

Keywords:   statistical regression, Bayesian approach, parametric approach, nonparametric approach, Bayesian Additive Regression Trees

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