A suite of generally applicable statistical methods based on empirical bootstrapping is presented for calculating uncertainty and testing the significance of quantitative differences in temperature and/or ice active site densities between ice nucleation temperature spectra derived from droplet freezing experiments. Such experiments are widely used to determine the heterogeneous ice nucleation properties and ice nucleation particle concentration spectra of different particle samples, as well as in studies of homogeneous freezing. Our methods avoid most of the assumptions and approximations inherent to existing approaches, and when sufficiently large sample sizes are used (approximately >150 droplets and $>=\mathrm{1000}$ bootstrap samples in our system), can capture the full range of random variability and error in ice nucleation spectra. Applications include calculation of accurate confidence intervals and confidence bands, quantitative statistical testing of differences between observed freezing spectra, accurate subtraction of the background filtered water freezing signal, and calculation of a range of statistical parameters using data from a single droplet array freezing experiment if necessary. By providing additional statistical tools to the community, this work will improve the quality and accuracy of statistical tests and representations of uncertainty in future ice nucleation research, and will allow quantitative comparisons of the ice nucleation ability of different particles and surfaces.

中文翻译：

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一种普遍适用的计算来自液滴冷冻实验的冰核光谱置信带的方法

提出了一套基于经验自举的普遍适用的统计方法，用于计算不确定性和测试从液滴冷冻实验得出的冰成核温度光谱之间温度和/或冰活性位点密度的定量差异的显着性。此类实验广泛用于确定不同颗粒样品的异质冰成核特性和冰成核颗粒浓度谱，以及均质冷冻研究。我们的方法避免了现有方法固有的大多数假设和近似值，并且当使用足够大的样本量时（大约>150个液滴和 $>=\mathrm{1000}$我们系统中的自举样本），可以捕获冰核光谱中的全部随机变化和误差。应用包括计算准确的置信区间和置信带，观察到的冷冻光谱之间差异的定量统计测试，背景过滤水冷冻信号的准确减法，以及必要时使用来自单个液滴阵列冷冻实验的数据计算一系列统计参数. 通过为社区提供额外的统计工具，这项工作将提高未来冰核研究中统计测试和不确定性表示的质量和准确性，并将允许对不同颗粒和表面的冰核能力进行定量比较。