Deterministic mathematical models, such as those specified via differential equations, are a powerful tool to communicate scientific insight. However, such models are necessarily simplified descriptions of the real world. Generalised Bayesian methodologies have been proposed for inference with misspecified models, but these are typically associated with vanishing parameter uncertainty as more data are observed. In the context of a misspecified deterministic mathematical model, this has the undesirable consequence that posterior predictions become deterministic and certain, while being incorrect. Taking this observation as a starting point, we propose Prediction-Centric Uncertainty Quantification, where a mixture distribution based on the deterministic model confers improved uncertainty quantification in the predictive context. Computation of the mixing distribution is cast as a (regularised) gradient flow of the maximum mean discrepancy (MMD), enabling consistent numerical approximations to be obtained. Results are reported on both a toy model from population ecology and a real model of protein signalling in cell biology.

翻译：确定性数学模型，例如通过微分方程指定的模型，是传达科学洞见的有力工具。然而，这类模型必然是对现实世界的简化描述。已有研究提出了用于错误设定模型推断的广义贝叶斯方法，但这些方法通常伴随着观测数据增多时参数不确定性趋于消失的特性。在错误设定的确定性数学模型背景下，这会导致一个不良后果：后验预测变得确定且肯定，但却是错误的。以此观察为出发点，我们提出了预测中心化不确定性量化方法，其中基于确定性模型的混合分布在预测情境中提供了改进的不确定性量化。混合分布的计算被构建为最大均值差异（MMD）的（正则化）梯度流，从而能够获得一致的数值近似。研究结果在一个来自种群生态学的玩具模型和一个关于细胞生物学中蛋白质信号传导的真实模型上进行了报告。