The multivariate adaptive regression spline (MARS) approach of Friedman (1991) and its Bayesian counterpart (Francom et al. 2018) are effective approaches for the emulation of computer models. The traditional assumption of Gaussian errors limits the usefulness of MARS, and many popular alternatives, when dealing with stochastic computer models. We propose a generalized Bayesian MARS (GBMARS) framework which admits the broad class of generalized hyperbolic distributions as the induced likelihood function. This allows us to develop tools for the emulation of stochastic simulators which are parsimonious, scalable, interpretable and require minimal tuning, while providing powerful predictive and uncertainty quantification capabilities. GBMARS is capable of robust regression with t distributions, quantile regression with asymmetric Laplace distributions and a general form of "Normal-Wald" regression in which the shape of the error distribution and the structure of the mean function are learned simultaneously. We demonstrate the effectiveness of GBMARS on various stochastic computer models and we show that it compares favorably to several popular alternatives.

翻译：弗里德曼（1991）提出的多元自适应回归样条（MARS）方法及其贝叶斯版本（Francom等，2018）是计算机模型仿真中的有效方法。传统的高斯误差假设限制了MARS及许多流行替代方法在处理随机计算机模型时的实用性。我们提出了一种广义贝叶斯MARS（GBMARS）框架，该框架将广义双曲分布这一广泛类别作为诱导似然函数。这使我们能够开发出用于随机模拟器的仿真工具，这些工具具有简约性、可扩展性、可解释性且需要最小化参数调整，同时具备强大的预测和不确定性量化能力。GBMARS能够通过t分布实现稳健回归，通过非对称拉普拉斯分布实现分位数回归，以及一种通用的"正态-瓦尔德"回归形式，其中误差分布的形状与均值函数的结构可同时学习。我们通过多种随机计算机模型展示了GBMARS的有效性，并证明其性能优于几种流行的替代方法。