Statistical models typically capture uncertainties in our knowledge of the corresponding real-world processes, however, it is less common for this uncertainty specification to capture uncertainty surrounding the values of the inputs to the model, which are often assumed known. We develop general modelling methodology with uncertain inputs in the context of the Bayes linear paradigm, which involves adjustment of second-order belief specifications over all quantities of interest only, without the requirement for probabilistic specifications. In particular, we propose an extension of commonly-employed second-order modelling assumptions to the case of uncertain inputs, with explicit implementation in the context of regression analysis, stochastic process modelling, and statistical emulation. We apply the methodology to a regression model for extracting aluminium by electrolysis, and emulation of the motivating epidemiological simulator chain to model the impact of an airborne infectious disease.

翻译：统计模型通常能够捕捉我们对相应真实世界过程知识中的不确定性，然而，这种不确定性规范较少涉及模型输入值中的不确定性——这些输入值通常被假定为已知。我们在贝叶斯线性范式框架下发展了含不确定输入的一般性建模方法论，该方法仅需对所有关注量进行二阶信念规范的调整，而无须概率规范要求。特别地，我们将常用二阶建模假设扩展至不确定输入情形，并在回归分析、随机过程建模及统计仿真中给出了显式实现。我们将该方法应用于电解法提取铝的回归模型，以及驱动性流行病学仿真链的统计仿真——该链用于模拟空气传播传染病的影响。