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We incorporate heteroskedasticity into Bayesian Additive Regression Trees (BART) by modeling the log of the error variance parameter as a linear function of prespecified covariates. Under this scheme, the Gibbs sampling procedure for the…

BART (Bayesian Additive Regression Trees) 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…

Ensemble learning is a statistical paradigm built on the premise that many weak learners can perform exceptionally well when deployed collectively. The BART method of Chipman et al. (2010) is a prominent example of Bayesian ensemble…

In the era of precision medicine, genome-wide epigenetic modifications offer rich data that could inform risk prediction. However, these data are high-dimensional and exhibit complex dependence structures, which makes it difficult to…

BCART (Bayesian Classification and Regression Trees) and BART (Bayesian Additive Regression Trees) are popular Bayesian regression models widely applicable in modern regression problems. Their popularity is intimately tied to the ability to…

Flexibly modeling how an entire density changes with covariates is an important but challenging generalization of mean and quantile regression. While existing methods for density regression primarily consist of covariate-dependent discrete…

Bayesian quadrature (BQ) is a method for solving numerical integration problems in a Bayesian manner, which allows users to quantify their uncertainty about the solution. The standard approach to BQ is based on a Gaussian process (GP)…

Regression discontinuity designs (RDD) are widely used for causal inference. In many empirical applications, treatment effects vary substantially with covariates, and ignoring such heterogeneity can lead to misleading conclusions, which…

This research aims to propose and evaluate a novel model named K-Fold Causal Bayesian Additive Regression Trees (K-Fold Causal BART) for improved estimation of Average Treatment Effects (ATE) and Conditional Average Treatment Effects…

Vector autoregressive (VAR) models assume linearity between the endogenous variables and their lags. This assumption might be overly restrictive and could have a deleterious impact on forecasting accuracy. As a solution, we propose…

In this paper we develop the randomized Sharded Bayesian Additive Regression Trees (SBT) model. We introduce a randomization auxiliary variable and a sharding tree to decide partitioning of data, and fit each partition component to a…

Bayesian Additive Regression Trees (BART) is a popular Bayesian non-parametric regression algorithm. The posterior is a distribution over sums of decision trees, and predictions are made by averaging approximate samples from the posterior.…

General circulation models (GCMs) are essential tools for climate studies. Such climate models may have varying accuracy across the input domain, but no model is uniformly best. One can improve climate model prediction performance by…

Individualized treatment rules (ITR) can improve health outcomes by recognizing that patients may respond differently to treatment and assigning therapy with the most desirable predicted outcome for each individual. Flexible and efficient…

Bayesian Causal Forests (BCF) is a causal inference machine learning model based on a highly flexible non-parametric regression and classification tool called Bayesian Additive Regression Trees (BART). Motivated by data from the Trends in…

In recent years, theoretical results and simulation evidence have shown Bayesian additive regression trees to be a highly-effective method for nonparametric regression. Motivated by cost-effectiveness analyses in health economics, where…

Count-compositional data arise in many different fields, including high-throughput sequencing experiments, ecological surveys, and palaeoclimate studies, where a common, important goal is to understand how covariates relate to the observed…

Ensembles of decision trees are a useful tool for obtaining for obtaining flexible estimates of regression functions. Examples of these methods include gradient boosted decision trees, random forests, and Bayesian CART. Two potential…

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…

For the discovery of regression relationships between Y and a large set of p potential predictors x 1 , . . . , x p , the flexible nonparametric nature of BART (Bayesian Additive Regression Trees) allows for a much richer set of…