论文标题
使用贝叶斯多项式近似的事先信息建模
Prior-informed Uncertainty Modelling with Bayesian Polynomial Approximations
论文作者
论文摘要
正交多项式近似构成了一组公认的不确定性定量方法的基础，称为多项式混乱。这些近似值为模拟各种计算工程应用中的物理系统提供了模型。在本文中，我们描述了能够在输入数据中纳入不确定性的多项式近似值的贝叶斯公式。通过分层结构的不同先验，这使我们可以通过不同的方法纳入有关推论任务的专家知识。这些包括模型中对稀疏性的信念；多项式系数（例如，通过低保真估计）或输出均值的近似知识，以及具有相似功能和/或物理行为的相关模型。我们表明，通过贝叶斯框架，可以利用这种先验知识来产生具有增强的预测精度的正交多项式近似值。
Orthogonal polynomial approximations form the foundation to a set of well-established methods for uncertainty quantification known as polynomial chaos. These approximations deliver models for emulating physical systems in a variety of computational engineering applications. In this paper, we describe a Bayesian formulation of polynomial approximations capable of incorporating uncertainties in input data. Through different priors in a hierarchical structure, this permits us to incorporate expert knowledge on the inference task via different approaches. These include beliefs of sparsity in the model; approximate knowledge of the polynomial coefficients (e.g. through low-fidelity estimates) or output mean, and correlated models that share similar functional and/or physical behaviours. We show that through a Bayesian framework, such prior knowledge can be leveraged to produce orthogonal polynomial approximations with enhanced predictive accuracy.
