Abstract
Bayesian additive regression trees (BART) has become increasingly popular as a flexible and scalable nonparametric regression approach for modern applied statistics problems. For the practitioner dealing with large and complex nonlinear response surfaces, its advantages include a matrix-free formulation and the lack of a requirement to prespecify a confining regression basis. Although flexible in fitting the mean, BART has been limited by its reliance on a constant variance error model. Alleviating this limitation, we propose HBART, a nonparametric heteroscedastic elaboration of BART. In BART, the mean function is modeled with a sum of trees, each of which determines an additive contribution to the mean. In HBART, the variance function is further modeled with a product of trees, each of which determines a multiplicative contribution to the variance. Like the mean model, this flexible, multidimensional variance model is entirely nonparametric with no need for the prespecification of a confining basis. Moreover, with this enhancement, HBART can provide insights into the potential relationships of the predictors with both the mean and the variance. Practical implementations of HBART with revealing new diagnostic plots are demonstrated with simulated and real data on used car prices and song year of release. Supplementary materials for this article are available online.
Original language | English (US) |
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Pages (from-to) | 405-417 |
Number of pages | 13 |
Journal | Journal of Computational and Graphical Statistics |
Volume | 29 |
Issue number | 2 |
DOIs | |
State | Published - Apr 2 2020 |
Keywords
- Applied statistical inference
- Big data
- Nonparametric regression
- Uncertainty quantification
ASJC Scopus subject areas
- Statistics and Probability
- Discrete Mathematics and Combinatorics
- Statistics, Probability and Uncertainty
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Dive into the research topics of 'Heteroscedastic BART via Multiplicative Regression Trees'. Together they form a unique fingerprint.Datasets
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Heteroscedastic BART via Multiplicative Regression Trees
Pratola, M. T. (Contributor), Chipman, H. A. (Contributor), George, E. I. (Contributor) & McCulloch, R. (Contributor), Taylor & Francis, 2021
DOI: 10.6084/m9.figshare.9954989, https://tandf.figshare.com/articles/dataset/Heteroscedastic_BART_Via_Multiplicative_Regression_Trees/9954989
Dataset
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Heteroscedastic BART Via Multiplicative Regression Trees
Pratola, M. T. (Contributor), Chipman, H. A. (Contributor), George, E. I. (Contributor) & McCulloch, R. (Contributor), Taylor & Francis, 2019
DOI: 10.6084/m9.figshare.9954989.v1, https://tandf.figshare.com/articles/Heteroscedastic_BART_Via_Multiplicative_Regression_Trees/9954989/1
Dataset
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Heteroscedastic BART via Multiplicative Regression Trees
Pratola, M. T. (Contributor), Chipman, H. A. (Contributor), George, E. I. (Contributor) & McCulloch, R. (Contributor), Taylor & Francis, 2019
DOI: 10.6084/m9.figshare.9954989.v2, https://tandf.figshare.com/articles/dataset/Heteroscedastic_BART_Via_Multiplicative_Regression_Trees/9954989/2
Dataset