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In recent years, there has been a considerable amount of work extending statistical theory to include the effects of distributed computation. This interest is fueled in part by the increased need to solve distributed statistical problems in fields such as wireless sensor networks (WSNs) and machine learning (ML). In WSNs, for example, one of the challenges is to use many redundant communication-constrained sensors to collect, communicate, and process data, in an efficient manner, for the purpose of solving a wide variety of problems, ranging from environmental to industrial monitoring (i.e. forest fire detection or pipeline health monitoring). An important aspect of such situations is their hierarchical communication architecture, something not yet addressed in the literature. We present our recent efforts to obtain bounds on the accuracy of statistical hypothesis testing in this domain.

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