Searching for as yet undetected γ $\gamma $ -ray sources is one of the main stated goals of the Fermi Large Area Telescope Collaboration. In this paper, we explore the capability of a filtering method based on a finite mixture of von Mises–Fisher distributions. The proposed procedure is specifically designed to handle data with support on the unit sphere. The assumption of a parametric model for each high energy emitting source allows us to derive an explicit expression for both the direction of the sources and their angular resolutions. The corresponding measures are based on the directional mean and the quantiles of the single mixture components. Sound criteria of model selection can provide an automatic way to determine the number of detected sources. Additionally, a likelihood-ratio test is developed to evaluate their significance. The procedure is tested on simulated data sets of photon emissions from high energy sources within the energy range [ 10 − 1 , 000 ] GeV $[10 - 1,000]\text{ GeV}$ . A real data example consisting of a sample of the Fermi LAT data collected over a period of about 7.2 years within the energy range [ 10 − 1 , 000 ] GeV $[10 - 1,000]\text{ GeV}$ , in a subregion of the γ $\gamma $ -ray sky, is furthermore provided.

中文翻译：

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一种使用 von Mises-Fisher 分布预过滤事件源的新方法

寻找尚未检测到的 γ $\gamma $ 射线源是费米大面积望远镜合作组织的主要既定目标之一。在本文中，我们探讨了基于 von Mises-Fisher 分布的有限混合的过滤方法的能力。建议的程序专门设计用于处理单位球体上的数据。每个高能发射源的参数模型假设使我们能够推导出源方向及其角分辨率的明确表达式。相应的度量基于方向均值和单个混合分量的分位数。模型选择的合理标准可以提供一种自动方式来确定检测到的源的数量。此外，还开发了似然比检验来评估其重要性。该程序在能量范围 [10 − 1 , 000 ] GeV $[10 - 1,000]\text{ GeV}$ 内的高能量源的光子发射模拟数据集上进行测试。一个真实的数据示例，包括在能量范围 [10 − 1 , 000 ] GeV $[10 - 1,000]\text{ GeV}$ 内，在大约 7.2 年的时间内收集的费米 LAT 数据样本，位于此外还提供了 γ $\gamma $ 射线天空。