Bayesian Additive Regression Trees with Basis-Expanded Functional Covariates

Area of Science:

• Environmental science
• Medical science
• Statistics

Background:

• Longitudinal data analysis is common in environmental science and medicine.
• Functional variables derived from dense time-series data offer rich insights.
• Traditional regression models have limitations when using functional covariates.

Purpose of the Study:

• To introduce Basis-Expanded Bayesian Additive Regression Trees (BBART).
• To enable the inclusion of functional covariates in regression models.
• To overcome limitations of existing functional regression methods.

Main Methods:

• Developed BBART, an adaptation of the original BART model.
• Leveraged BART's strengths for flexible modeling.
• Utilized Markov Chain Monte Carlo (MCMC) for posterior inference.

Main Results:

• BBART allows for the inclusion of functional covariates.
• The method does not assume additivity or smooth effects.
• Posterior inference is enabled through MCMC samples.

Conclusions:

• BBART offers a flexible and powerful approach for regression with functional covariates.
• This method enhances the utility of time-series data in environmental and medical research.
• BBART provides a robust alternative to traditional functional regression models.