Suppose we observe a Poisson process in real time for which the intensity may take on two possible values $\lambda_0$ and $\lambda_1$. Suppose further that the priori probability of the true intensity is not given. We solve a minimax version of Bayesian problem of sequential testing of two simple hypotheses to minimize a linear combination of the probability of wrong detection and the expected waiting time in the worst scenario of all possible priori distributions. An equivalent characterization for the least favorable distributions is derived and a sufficient condition for the existence is concluded.

翻译：假设我们实时观测一个强度可能取两个值 $\lambda_0$ 和 $\lambda_1$ 的泊松过程，且未给定该真实强度的先验概率。我们求解贝叶斯问题中两个简单假设序贯检验的极小极大版本，以在所有可能先验分布的最坏情形下最小化错误检测概率与期望等待时间的线性组合。推导出最不利分布的等价刻画，并得出其存在的充分条件。