Online multiple testing with e-values
International Conference on Artificial Intelligence and Statistics(2023)
摘要
A scientist tests a continuous stream of hypotheses over time in the course
of her investigation -- she does not test a predetermined, fixed number of
hypotheses. The scientist wishes to make as many discoveries as possible while
ensuring the number of false discoveries is controlled -- a well recognized way
for accomplishing this is to control the false discovery rate (FDR). Prior
methods for FDR control in the online setting have focused on formulating
algorithms when specific dependency structures are assumed to exist between the
test statistics of each hypothesis. However, in practice, these dependencies
often cannot be known beforehand or tested after the fact. Our algorithm,
e-LOND, provides FDR control under arbitrary, possibly unknown, dependence. We
show that our method is more powerful than existing approaches to this problem
through simulations. We also formulate extensions of this algorithm to utilize
randomization for increased power, and for constructing confidence intervals in
online selective inference.
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