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The increasing prevalence and utility of large, public databases necessitatesthe development of appropriate methods for controlling false discovery.Motivated by this challenge, we discuss the generic problem of testing apossibly infinite stream of null hypotheses. In this context, Foster and Stine(2008) suggested a novel method named Alpha Investing for controlling a falsediscovery measure known as mFDR. We develop a more general procedure forcontrolling mFDR, of which Alpha Investing is a special case. We show that incommon, practical situations, the general procedure can be optimized to producean expected reward optimal (ERO) version, which is more powerful than AlphaInvesting.  We then present the concept of quality preserving databases (QPD), originallyintroduced in Aharoni et al. (2011), which formalizes efficient public databasemanagement to simultaneously save costs and control false discovery. We showhow one variant of generalized alpha investing can be used to control mFDR in aQPD and lead to significant reduction in costs compared to naive approaches forcontrolling the Family-Wise Error Rate implemented in Aharoni et al. (2011).

Generalized Alpha Investing: Definitions, Optimality Results, and Application to Public Databases