Approximating significance scans of searches for new particles in high-energy physics experiments as Gaussian fields is a well-established way to estimate the trials factors required to quantify global significances. We propose a novel, highly efficient method to estimate the covariance matrix of such a Gaussian field. The method is based on the linear approximation of statistical fluctuations of the signal amplitude. For one-dimensional searches the upper bound on the trials factor can then be calculated directly from the covariance matrix. For higher dimensions, the Gaussian process described by this covariance matrix may be sampled to calculate the trials factor directly. This method also serves as the theoretical basis for a recent study of the trials factor with an empirically constructed set of Asmiov-like background datasets. We illustrate the method with studies of a $H \rightarrow \gamma \gamma$ inspired model that was used in the empirical paper.

翻译：将高能物理实验中新粒子搜寻的显著性扫描近似为高斯场，是估算全局显著性所需试验因子的一种成熟方法。我们提出了一种新颖且高效的方法来估算此类高斯场的协方差矩阵。该方法基于信号幅度统计涨落的线性近似。对于一维搜索，试验因子的上限可直接由该协方差矩阵计算得出。对于更高维度，可通过采样该协方差矩阵所描述的高斯过程直接计算试验因子。该方法同时也为近期一项基于经验构造的类Asmiov背景数据集研究试验因子的工作提供了理论基础。我们通过实证论文中使用的$H \rightarrow \gamma \gamma$启发模型对该方法进行了说明。