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We consider two related data screening problems: one is to find the smallest subset such that it virtually contains all signals and another is to find the largest subset such that it essentially contains only signals. These screening problems are closely connected to but distinct from the more conventional signal detection or multiple-testing problems. We develop phase transition diagrams to characterize the fundamental limits in simultaneous inference and derive data-driven screening procedures which control the error rates with near optimality properties. Applications in the context of multistage high throughput studies are discussed.<\/jats:p>","DOI":"10.1111\/rssb.12171","type":"journal-article","created":{"date-parts":[[2016,3,21]],"date-time":"2016-03-21T04:42:43Z","timestamp":1458535363000},"page":"197-223","source":"Crossref","is-referenced-by-count":20,"title":["Optimal Screening and Discovery of Sparse Signals with Applications to Multistage High Throughput Studies"],"prefix":"10.1093","volume":"79","author":[{"given":"T.","family":"Tony Cai","sequence":"first","affiliation":[{"name":"University of Pennsylvania , Philadelphia , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenguang","family":"Sun","sequence":"additional","affiliation":[{"name":"University of Southern California , Los Angeles , USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2016,3,20]]},"reference":[{"key":"2023021801102855200_rssb12171-cit-0001","doi-asserted-by":"crossref","first-page":"4004","DOI":"10.1073\/pnas.0910781107","article-title":"Ultrahigh-throughput screening in drop-based microfluidics for directed evolution","volume":"107","author":"Agresti","year":"2010","journal-title":"Proc. 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