The complexity underlying real-world systems implies that standard statistical hypothesis testing methods may not be adequate for these peculiar applications. Specifically, we show that the likelihood-ratio (LR) test’s null-distribution needs to be modified to accommodate the complexity found in multi-edge network data. When working with independent observations, the p-values of LR tests are approximated using a χ ² distribution. However, such an approximation should not be used when dealing with multi-edge network data. This type of data is characterized by multiple correlations and competitions that make the standard approximation unsuitable. We provide a solution to the problem by providing a better approximation of the LR test null-distribution through a beta distribution. Finally, we empirically show that even for a small multi-edge network, the standard χ ² approximation provides erroneous results, while the proposed beta approximation yields the correct p-value estimation.

现实世界系统的复杂性意味着标准的统计假设检验方法可能不足以满足这些特殊的应用。具体来说，我们表明需要修改似然比 (LR) 测试的零分布以适应在多边网络数据中发现的复杂性。在处理独立观测值时，LR 检验的p值使用χ ²近似分配。但是，在处理多边网络数据时不应该使用这种近似值。这种类型的数据具有多重相关性和竞争性，这使得标准近似不合适。我们通过 beta 分布提供了 LR 测试零分布的更好近似，从而为该问题提供了解决方案。最后，我们凭经验表明，即使对于小型多边网络，标准的χ ²近似也会提供错误的结果，而建议的 beta 近似会产生正确的p值估计。