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Abstract:
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When applying statistical methods in the basic sciences it has become increasingly relevant to care about the replicability of deductive associations. In doing so, often along with the primary z-scores or p-values, auxiliary covariates are available. This auxiliary information, when carefully accounted, may improve the power of replicability analysis. We present an empirical Bayes framework of estimating replicability in the presence of covariates. In the framework considered, our approach is asymptotically optimal. Through several numerical experiments, we demonstrate the finite-sample gain in power. The method is illustrated in several applications. This work may be viewed as a way of incorporating covariate information in large-scale multiple testing or controlling the false discovery rate framework, however, with the central goal of protecting replicability. When primary and auxiliary scientific data are available from multiple studies, such an analysis would be vital.
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