r-Power for Multiple Hypotheses Testing under Dependence

In an era of "big data" the challenge of managing large-scale multiplicity in statistical analysis has become increasingly crucial. The concept of r-power, introduced Dasgupta et al. (2016), presents an innovative approach to addressing multiplicity with focus on the reliability of selecting a relevant list of hypotheses. This manuscript advances the r-power conversation by relaxing the original assumption of independence among hypotheses to accommodate a block diagonal correlation structure. Through analytical exploration and validation via simulations, we unveil how the underlying dependence structure influences r-power. Our findings illuminate the nuanced role that dependence plays in the reliability of hypothesis selection, offering a deeper understanding and novel perspectives on managing multiplicity in large datasets. Furthermore, we highlight the practicality and applicability of our results in the context of a Genome-Wide Association