关于线性区分组检验的后代分布的注记
Note on the offspring distribution for group testing in the linear regime
摘要：
群体测试问题涉及在大量$n$人群中识别一小组$k$感染个体。在我们的处置是一个测试计划，可以测试群体的个人。当且仅当至少有一个人被感染时，测试才呈阳性。在这篇文章中，我们为分析$k$在$n$中线性缩放时的群体测试的信念传播奠定了基础。为此，我们推导出不同类型个体的后代分布。有了这些分布，我们可以使用种群动力学算法来模拟置信传播产生的后验边缘分布。
英文摘要：
The group testing problem is concerned with identifying a small set of $k$ infected individuals in a large population of $n$ people. At our disposal is a testing scheme that can test groups of individuals. A test comes back positive if and only if at least one individual is infected. In this note, we lay groundwork for analysing belief propagation for group testing when $k$ scales linearly in $n$. To this end, we derive the offspring distribution for different types of individuals. With these distributions at hand, one can employ the population dynamics algorithm to simulate the posterior marginal distribution resulting from belief propagation.
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。
