Title: Multistage Adaptive Testing of Sparse Signals,
Abstract: 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.