In high-energy physics it is a recurring challenge to efficiently and precisely (enough) calculate the global significance of, e.g., a potential new resonance. We propose a new method that models the significance in the search region as a Gaussian Process. The kernel of the Gaussian Process is approximated with a covariance matrix and is calculated with a carefully designed set of background-only data sets, comparable in number to the random background-only data sets used in a typical analysis that relies on the average upcrossings of the significance. The trials factor for both low and moderate significances can subsequently be calculated to the desired precision with a computationally inexpensive random sampling of the Gaussian Process. In addition, once the covariance of the Gaussian Process is determined, the average number of upcrossings can be computed analytically. In our work we give some highlights of the analytic calculation and also discuss some peculiarities of the trials factor estimation on a finite grid. We illustrate the method with studies of three complementary statistical models.

翻译：在高能物理中，高效且足够精确地计算潜在新共振等信号的全局显著性始终是一项挑战。我们提出了一种新方法，将搜寻区域内的显著性建模为高斯过程。该高斯过程的核函数通过协方差矩阵近似，并利用精心设计的仅含背景的样本集进行计算，其样本数量与依赖于显著性平均上穿次数的典型分析中所用的随机仅含背景样本集相当。随后，通过计算成本低廉的高斯过程随机采样，可达到所需精度地计算低显著性及中等显著性的搜寻因子。此外，一旦确定高斯过程的协方差，即可解析计算平均上穿次数。本研究展示了部分解析计算的亮点，并讨论了有限网格上搜寻因子估计的一些特殊性质。我们通过三个互补统计模型的研究对该方法进行了说明。