自校正别处效应：使用峰高快速评估统计显著性
Self-Calibrating the Look-Elsewhere Effect: Fast Evaluation of the Statistical Significance Using Peak Heights
摘要：
在实验中，人们搜索一个大的参数空间的异常，人们经常发现许多虚假的噪声引起的峰值的可能性。这就是所谓的“别处看”效应，在进行统计分析时必须加以纠正。本文介绍了一种方法来校准的虚警概率（FAP），或$p$值，为一个给定的数据集，通过考虑的最高峰的高度的可能性。在自校准的最简单形式中，物理峰的别处查找校正的$χ^2$由峰的$χ^2$减去最高噪声引起的峰的$χ^2$来近似。将这一概念推广到考虑较低的峰提供了一种快速量化统计显著性并提高准确性的方法。与其他方法相比，这种方法的计算成本可以忽略不计，因为可能性中的峰值是每个峰值搜索分析的副产品。我们适用于天文学的例子，包括行星探测，周期图和宇宙学。
英文摘要：
In experiments where one searches a large parameter space for an anomaly, one often finds many spurious noise-induced peaks in the likelihood. This is known as the look-elsewhere effect, and must be corrected for when performing statistical analysis. This paper introduces a method to calibrate the false alarm probability (FAP), or $p$-value, for a given dataset by considering the heights of the highest peaks in the likelihood. In the simplest form of self-calibration, the look-elsewhere-corrected $χ^2$ of a physical peak is approximated by the $χ^2$ of the peak minus the $χ^2$ of the highest noise-induced peak. Generalizing this concept to consider lower peaks provides a fast method to quantify the statistical significance with improved accuracy. In contrast to alternative methods, this approach has negligible computational cost as peaks in the likelihood are a byproduct of every peak-search analysis. We apply to examples from astronomy, including planet detection, periodograms, and cosmology.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
