Model Mixing Using Bayesian Additive Regression Trees

Abstract

In modern computer experiment applications, one often encounters the situation where various models of a physical system are considered, each implemented as a simulator on a computer. An important question in such a setting is determining the best simulator, or the best combination of simulators, to use for prediction and inference. Bayesian model averaging (BMA) and stacking are two statistical approaches used to account for model uncertainty by aggregating a set of predictions through a simple linear combination or weighted average. Bayesian model mixing (BMM) extends these ideas to capture the localized behavior of each simulator by defining input-dependent weights. One possibility is to define the relationship between inputs and the weight functions using a flexible nonparametric model that learns the local strengths and weaknesses of each simulator. This article proposes a BMM model based on Bayesian Additive Regression Trees (BART). The proposed methodology is applied to combine predictions from Effective Field Theories (EFTs) associated with a motivating nuclear physics application. Supplementary materials for this article are available online. Source code is available at https://github.com/jcyannotty/OpenBT.

KEYWORDS:

• Computer experiments
• Effective field theories
• Model stacking
• Uncertainty quantification

Supplementary Materials

The supplementary material includes the essential derivations of the methodology along with additional information regarding EFTs. Code implementing the method and reproducing the examples is also available online.

Acknowledgments

The authors would like to thank the Editor, an Associate Editor, and two referees for helpful comments on this work.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work of JCY and RJF work was supported in part by the National Science Foundation under Agreement OAC-2004601. The work of MTP was supported in part by the National Science Foundation under Agreements DMS-1916231, DMS-1564395, OAC-2004601, and in part by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No. OSR-2018-CRG7-3800.3. The work of TJS was supported in part by the National Science Foundation under Agreement DMS-1564395 (The Ohio State University).