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.

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注意在线性方案中进行小组测试的后代分布

小组测试问题与在大量$ n $人群中识别出少数受k $感染的个体有关。我们可以使用一种可以测试个人群体的测试方案。当且仅当至少一个人被感染时，测试才返回阳性。在本说明中，我们为在$ k $线性缩放$ n $时进行群测试分析信念传播奠定了基础。为此，我们推导了不同类型个体的后代分布。有了这些分布，就可以采用总体动力学算法来模拟因信念传播而产生的后边缘分布。