Multistage design has been used in a wide range of scientific fields. By allocating sensing resources adaptively, one can effectively eliminate null locations and localize signals with a smaller study budget. We formulate a decision-theoretic framework for simultaneous multi-stage adaptive testing and study how to minimize the total number of measurements while meeting pre-specified constraints on both the false positive rate (FPR) and missed discovery rate (MDR). The new procedure, which effectively pools information across individual tests using a simultaneous multistage adaptive ranking and thresholding (SMART) approach, can achieve precise error rates control and lead to great savings in total study costs. Numerical studies confirm the effectiveness of SMART for FPR and MDR control and show that it achieves substantial power gain over existing methods. The SMART procedure is demonstrated through the analysis of high-throughput screening data and spatial imaging data.
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