在多维搜索中估计信号的重要性
Estimating the significance of a signal in a multi-dimensional search
摘要：
在旨在探测天体物理学来源的实验中，如中微子望远镜，人们通常在连续的参数空间（例如天空的角坐标，可能还有时间）上进行搜索，寻找与背景假设最显著的偏差。这样的程序固有地涉及“看别处效应”，即在搜索范围内的任何地方出现类似信号的波动的可能性。因此，正确地估计给定观测的$p$值需要对整个搜索进行重复模拟，这是一个在CPU资源方面可能过度膨胀的过程。最近的结果从理论的随机场提供了强大的工具，可用于减轻这一困难，在广泛的应用。我们回顾了这些结果，并讨论了它们的实现，与一个详细的例子应用于中微子点源分析的冰立方实验。
英文摘要：
In experiments that are aimed at detecting astrophysical sources such as neutrino telescopes, one usually performs a search over a continuous parameter space (e.g. the angular coordinates of the sky, and possibly time), looking for the most significant deviation from the background hypothesis. Such a procedure inherently involves a "look elsewhere effect", namely, the possibility for a signal-like fluctuation to appear anywhere within the search range. Correctly estimating the $p$-value of a given observation thus requires repeated simulations of the entire search, a procedure that may be prohibitively expansive in terms of CPU resources. Recent results from the theory of random fields provide powerful tools which may be used to alleviate this difficulty, in a wide range of applications. We review those results and discuss their implementation, with a detailed example applied for neutrino point source analysis in the IceCube experiment.
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