  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, controls the error rates and leads to great
savings in total study costs. Numerical studies confirm the effectiveness of
SMART. The SMART procedure is illustrated through the analysis of large-scale
A/B tests, high-throughput screening and image analysis.
