哪些建模选择塑造了你的插值图？地下水硫酸盐浓度的最优传输敏感性分析
Which modelling choices shape your interpolation map? An Optimal Transport sensitivity analysis for groundwater sulfate concentration
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中文总结 AI 辅助
本研究提出一种基于最优传输的全局敏感性分析方法，将空间预测图的不确定性归因于建模选择，并应用于巴黎盆地地下水硫酸盐浓度制图，发现协变量选择和网格分辨率是主要不确定性来源。
中文摘要 AI 辅助
空间预测图对于环境管理至关重要，但对主观建模选择（如协变量、空间依赖结构或网格分辨率）高度敏感。我们开发了一个工作流程，将由此产生的地图不确定性归因于这些选择，并适用于任何空间模型，因为它仅作用于通过将选择传播到空间预测中而生成的地图集合。然后对该集合进行过滤，仅保留具有可接受预测性能的模型，通过主成分（PC）分析降低维度，并基于最优传输（OT）度量通过全局敏感性分析量化所得得分对每个选择的敏感性。我们使用贝叶斯地质统计学对法国巴黎盆地地下水中硫酸盐浓度的空间制图进行了框架演示，这对于评估地下水化学质量和建立含水层的自然地球化学基线至关重要。对于此应用，协变量、网格分辨率、协方差模型和先验被组合成18000个候选配置。这些配置通过交叉验证的均方根误差（RMSE）和预测区间的95%覆盖率进行过滤，然后保留的配置在高分辨率网格上进行推断并缩减为其三个主成分。OT分析确定协变量选择（在95%覆盖率下）和网格分辨率（在RMSE下）是主成分不确定性的主要来源，而协方差模型的选择对不确定性的贡献可忽略不计。
英文摘要
Spatial prediction maps are crucial for environmental management yet highly sensitive to subjective modelling choices such as, e.g., covariates, spatial dependence structures, or mesh resolution. We develop a workflow that attributes the resulting map uncertainty to these choices and is applicable to any spatial model, since it operates only on an ensemble of maps produced by propagating the choices through spatial prediction. This ensemble is then filtered to retain only models with acceptable predictive performance, reduced in dimension by principal component (PC) analysis, and the sensitivity of the resulting scores to each choice is quantified by global sensitivity analysis based on optimal transport (OT) metrics. We demonstrate the framework with Bayesian geostatistics applied to the spatial mapping of sulphate concentrations in groundwater of Paris Basin (France), which is key for assessing groundwater chemical quality and establishing the natural geochemical baseline of aquifers. For this application, the covariates, mesh resolution, covariance models, and priors are combined into 18000 candidate configurations. These are filtered by cross-validated root mean square error (RMSE) and 95% coverage of the prediction interval, and the retained configurations are then inferred on a high-resolution grid and reduced to its three PCs. The OT analysis identifies covariate selection (under 95% coverage) and mesh resolution (under RMSE) as the dominant sources of uncertainty to the PCs, and a negligible one for the choice of the covariance model.
