In this work, we study the problem of testing the marginal distributions of multiple independent, sequentially observed data streams, where for each stream there are multiple candidate hypotheses to select from, in the presence of prior information on the unknown hypothesis configuration. The goal is to understand the benefit of such information and to design a sequential testing procedure that effectively leverages it. We start with arbitrary prior information and specialize to concrete examples, including known number or known lower bound on the number of streams following each hypothesis, and the presence of exclusive hypotheses. The designed procedure is three-fold: (i) reliable, i.e., controlling all types of familywise error probabilities below arbitrary user-specified levels, (ii) computationally efficient, i.e., focusing on minimal sets of alternative hypothesis configurations in making decisions, and (iii) asymptotically optimal, i.e., achieving the minimum expected sample size among all reliable procedures asymptotically as the error levels go to zero. Numerical studies are presented for illustration.

翻译：本文研究在存在未知假设构型先验信息的情况下，对多个独立序贯观测数据流的边际分布进行检验的问题，每个数据流对应多个候选假设。目标是理解此类信息的效用，并设计能有效利用该信息的序贯检验程序。我们从一般先验信息出发，并将其具体化至典型场景，包括已知或已知下界的各假设对应的数据流数量，以及存在互斥假设的情况。设计的程序具有三重特性：（i）可靠性——能将各类族系错误概率控制在用户指定的任意水平以下；（ii）计算高效性——在决策时聚焦于最小备选假设构型集；（iii）渐近最优性——当错误概率趋于零时，能渐近地达到所有可靠程序中最小期望样本量。最后通过数值算例进行验证。