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 non-parametric model that learns the local strengths and weaknesses of each simulator. This paper 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.

翻译：在现代计算机实验应用中，常会遇到对一个物理系统考虑多种模型的情况，每种模型均作为模拟器在计算机上实现。在此类设定中，一个重要问题是确定最佳模拟器或最佳模拟器组合，以用于预测和推断。贝叶斯模型平均（BMA）和堆叠是两种通过简单线性组合或加权平均聚合一组预测结果来考虑模型不确定性的统计方法。贝叶斯模型混合（BMM）扩展了这些思想，通过定义依赖于输入的权重来捕捉每个模拟器的局部行为。一种可能性是使用灵活的非参数模型学习每个模拟器的局部优势与劣势，从而定义输入与权重函数之间的关系。本文提出了一种基于贝叶斯加性回归树（BART）的BMM模型。所提出的方法被应用于结合与一项核物理应用相关的有效场论（EFTs）的预测结果。