Uncertainty quantification is an important topic for many environmental studies, such as identifying zones where potentially toxic materials exist in the soil. In this work, the nonparametric geostatistical framework of histogram via entropy reduction (HER) is adapted to address local and spatial uncertainty in the context of risk of soil contamination. HER works with empirical probability distributions, coupling information theory and probability aggregation methods to estimate conditional distributions, which gives it the flexibility to be tailored for different data and application purposes. To explore how HER can be used for estimating threshold-exceeding probabilities, it is applied to map the risk of soil contamination by lead in the well-known dataset of the region of Swiss Jura. Its results are compared to indicator kriging (IK) and to an ordinary kriging (OK) model available in the literature. For the analyzed dataset, IK and HER predictions achieve the best performance and exhibit comparable accuracy and precision. Compared to IK, advantages of HER for uncertainty estimation in a fine resolution are that it does not require modeling of multiple indicator variograms, correcting order-relation violations, or defining interpolation/extrapolation of distributions. Finally, to avoid the well-known smoothing effect when using point estimations (as is the case with both kriging and HER), and to provide maps that reflect the spatial fluctuation of the observed reality, we demonstrate how HER can be used in combination with sequential simulation to assess spatial uncertainty (uncertainty jointly over several locations).

不确定性量化是许多环境研究的重要主题，例如识别土壤中存在潜在有毒物质的区域。在这项工作中，通过熵减少 (HER) 的直方图的非参数地质统计框架适用于解决土壤污染风险背景下的局部和空间不确定性。HER 使用经验概率分布、耦合信息理论和概率聚合方法来估计条件分布，这使其能够灵活地针对不同的数据和应用目的进行定制。为了探索如何使用 HER 来估计超过阈值的概率，它被用于绘制瑞士侏罗地区著名数据集中铅污染的风险图。将其结果与指标克里金法 (IK) 和文献中可用的普通克里金法 (OK) 模型进行比较。对于分析的数据集，IK 和 HER 预测实现了最佳性能并表现出相当的准确性和精确度。与 IK 相比，HER 在精细分辨率下进行不确定性估计的优势在于它不需要对多个指标变异函数进行建模、纠正顺序关系违规或定义分布的内插/外推。最后，为了避免使用点估计时众所周知的平滑效应（就像克里金法和 HER 的情况一样），并提供反映观察到的现实空间波动的地图，我们演示了如何将 HER 与连续模拟以评估空间不确定性（多个位置的联合不确定性）。