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（如通过微分方程指定的模型）是传达科学见解的有力工具。然而，此类模型必然是对现实世界的简化描述。广义贝叶斯方法已被提出用于处理误设模型的推断问题，但这些方法通常伴随着参数不确定性随观测数据增加而消失的特性。在误设定性数学模型的背景下，这会导致一个不良后果：后验预测变得确定且确信，但却是错误的。以此为出发点，我们提出了预测中心化不确定性量化方法，该方法基于确定性模型构建混合分布，从而在预测情境中实现改进的不确定性量化。混合分布的计算被表述为最大均值差异（MMD）的（正则化）梯度流，使得能够获得一致的数值近似解。研究结果在种群生态学的玩具模型和细胞生物学中蛋白质信号传导的真实模型上均得到了验证。