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Bayesian Additive Regression Trees (BART) are non-parametric models that can capture complex exogenous variable effects. In any regression problem, it is often of interest to learn which variables are most active. Variable activity in BART…

Methodology · Statistics 2020-09-16 Akira Horiguchi , Matthew T. Pratola , Thomas J. Santner

Medical prediction applications often need to deal with small sample sizes compared to the number of covariates. Such data pose problems for prediction and variable selection, especially when the covariate-response relationship is…

Machine Learning · Statistics 2024-11-05 Jeroen M. Goedhart , Thomas Klausch , Jurriaan Janssen , Mark A. van de Wiel

Additive regression trees are flexible non-parametric models and popular off-the-shelf tools for real-world non-linear regression. In application domains, such as bioinformatics, where there is also demand for probabilistic predictions with…

Machine Learning · Statistics 2015-02-17 Balaji Lakshminarayanan , Daniel M. Roy , Yee Whye Teh

Measurement error is prevalent across all domains of scientific research where only imprecise observations, rather than the true underlying values, can be obtained. For example, estimates of human microbiome diversity are based on small…

Methodology · Statistics 2026-03-10 Kevin McCoy , Zachary Wooten , Christine B. Peterson

The Bayesian additive regression trees (BART) model is an ensemble method extensively and successfully used in regression tasks due to its consistently strong predictive performance and its ability to quantify uncertainty. BART combines…

Methodology · Statistics 2023-09-18 Mateus Maia , Keefe Murphy , Andrew C. Parnell

The effectiveness of Bayesian Additive Regression Trees (BART) has been demonstrated in a variety of contexts including non-parametric regression and classification. A BART scheme for estimating the intensity of inhomogeneous Poisson…

Statistics Theory · Mathematics 2022-11-15 Stamatina Lamprinakou , Mauricio Barahona , Seth Flaxman , Sarah Filippi , Axel Gandy , Emma McCoy

Tree-based regression and classification has become a standard tool in modern data science. Bayesian Additive Regression Trees (BART) has in particular gained wide popularity due its flexibility in dealing with interactions and non-linear…

Computation · Statistics 2022-09-13 Alan Inglis , Andrew Parnell , Catherine Hurley

We present a Bayesian nonparametric model for conditional distribution estimation using Bayesian additive regression trees (BART). The generative model we use is based on rejection sampling from a base model. Typical of BART models, our…

Methodology · Statistics 2022-02-02 Yinpu Li , Antonio R. Linero , Jared S. Murray

Dealing with missing data poses significant challenges in predictive analysis, often leading to biased conclusions when oversimplified assumptions about the missing data process are made. In cases where the data are missing not at random…

Methodology · Statistics 2024-12-20 Yong Chen Goh , Wuu Kuang Soh , Andrew C. Parnell , Keefe Murphy

Techniques to reduce the energy burden of an industrial ecosystem often require solving a multiobjective optimization problem. However, collecting experimental data can often be either expensive or time-consuming. In such cases, statistical…

Machine Learning · Computer Science 2021-09-07 Akira Horiguchi , Thomas J. Santner , Ying Sun , Matthew T. Pratola

We propose a simple yet powerful extension of Bayesian Additive Regression Trees which we name Hierarchical Embedded BART (HE-BART). The model allows for random effects to be included at the terminal node level of a set of regression trees,…

Methodology · Statistics 2023-04-25 Bruna Wundervald , Andrew Parnell , Katarina Domijan

Few methods in Bayesian non-parametric statistics/ machine learning have received as much attention as Bayesian Additive Regression Trees (BART). While BART is now routinely performed for prediction tasks, its theoretical properties began…

Statistics Theory · Mathematics 2019-05-10 Veronika Rockova

There is a dearth of robust methods to estimate the causal effects of multiple treatments when the outcome is binary. This paper uses two unique sets of simulations to propose and evaluate the use of Bayesian Additive Regression Trees…

Methodology · Statistics 2020-01-22 Liangyuan Hu , Chenyang Gu , Michael Lopez , Jiayi Ji , Juan Wisnivesky

Bayesian Additive Regression Trees (BART) is a popular Bayesian non-parametric regression model that is commonly used in causal inference and beyond. Its strong predictive performance is supported by well-developed estimation theory,…

Machine Learning · Statistics 2026-02-10 Yan Shuo Tan , Omer Ronen , Theo Saarinen , Bin Yu

The study of dependence between random variables under external influences is a challenging problem in multivariate analysis. We address this by proposing a novel semi-parametric approach for conditional copula models using Bayesian…

Methodology · Statistics 2026-03-11 Tathagata Basu , Fabrizio Leisen , Cristiano Villa , Kevin Wilson

We develop a Bayesian non-parametric quantile panel regression model. Within each quantile, the response function is a convex combination of a linear model and a non-linear function, which we approximate using Bayesian Additive Regression…

Econometrics · Economics 2021-10-08 Todd E. Clark , Florian Huber , Gary Koop , Massimiliano Marcellino , Michael Pfarrhofer

This article proposes a novel framework that integrates Bayesian Additive Regression Trees (BART) into a Factor-Augmented Vector Autoregressive (FAVAR) model to forecast macro-financial variables and examine asymmetries in the transmission…

Econometrics · Economics 2025-06-16 Sofia Velasco

Bayesian Additive Regression Trees (BART) is a statistical sum of trees model. It can be considered a Bayesian version of machine learning tree ensemble methods where the individual trees are the base learners. However for data sets where…

Distribution regression, where the goal is to predict a scalar response from a distribution-valued predictor, arises naturally in settings where observations are grouped and outcomes depend on group-level characteristics rather than on…

Methodology · Statistics 2026-03-09 Antonio R. Linero , Soumyabrata Bose , Jared Murray

In many longitudinal studies, the covariate and response are often intermittently observed at irregular, mismatched and subject-specific times. How to deal with such data when covariate and response are observed asynchronously is an often…

Methodology · Statistics 2021-08-27 Hao Ran , Yang Bai