Group testing is an active area of current research and has important applications in medicine, biotechnology, genetics, and product testing. There have been recent advances in design and estimation, but the simple Dorfman procedure introduced by R. Dorfman in 1943 is widely used in practice. In many practical situations, the exact value of the probability p of being affected is unknown. We present both minimax and Bayesian solutions for the group size problem when p is unknown. For unbounded p, we show that the minimax solution for group size is 8, while using a Bayesian strategy with Jeffreys’ prior results in a group size of 13. We also present solutions when p is bounded from above. For the practitioner, we propose strong justification for using a group size of between 8 and 13 when a constraint on p is not incorporated and provide useable code for computing the minimax group size under a constrained p.

中文翻译：

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关于两阶段群测试问题的极大极小解的注解

群体测试是当前研究的一个活跃领域，在医学、生物技术、遗传学和产品测试中有着重要的应用。最近在设计和估计方面取得了进展，但 R. Dorfman 在 1943 年引入的简单 Dorfman 程序在实践中得到了广泛应用。在许多实际情况中，受影响概率 p 的确切值是未知的。当 p 未知时，我们为组大小问题提供了极大极小和贝叶斯解决方案。对于无界 p，我们表明组大小的极小极大解为 8，同时使用贝叶斯策略和 Jeffreys 的先验结果，组大小为 13。我们还提供了当 p 从上方有界时的解决方案。对于练习者来说，