🤖 AI Summary
为解决标量场数据中特征提取的不确定性表示问题，提出了一种基于Hoeffding不等式的分布无关置信带方法，以提供更准确的不确定性可视化。
📝 Abstract
Uncertainty visualization has been shown to be pivotal for conveying the reliability of features extracted from scalar fields. Features represented by isocontours, mean isocontours lack an indication of spatial uncertainty, whereas spaghetti isocontour plots can become cluttered and difficult to interpret. Existing methods relying on specific distribution assumptions, such as Gaussian and nonparametric bootstrap, to provide compact clutter-free spatial confidence bounds but may underestimate uncertainty for ensembles with a limited number of samples. We introduce a robust, distribution-agnostic Hoeffding confidence band as a novel complementary (and not competitive) technique to mitigate potentially misleading uncertainty bounds that may arise from distribution-based assumptions. The approach constructs vertex-wise confidence bounds using Hoeffding's inequality and propagates them to generate isocontour confidence bands. Results on synthetic and real ensemble datasets show that the Hoeffding confidence bands are loose but accurately capture underlying true values that may be missed by the Gaussian and bootstrap alternatives while remaining computationally efficient.