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.
翻译:群体测试问题涉及在一大批人口(一美元)中识别一小批一美元感染者。我们掌握的是一种测试计划,可以测试个人群体。如果而且只有在至少一名个人被感染的情况下,测试才会恢复为阳性。在本说明中,我们为分析群体测试中的信仰传播奠定了基础,当以美元线性计算以美元计算时。为此,我们得出不同类型个人的后代分布。有了这些分布,人们可以使用人口动态算法模拟信仰传播产生的后期边缘分布。