  This paper explores the intrinsic connections between the Bayesian false
discovery rate (FDR) control procedures and their counterpart of frequentist
procedures. We attempt to offer a unified view of FDR control within and beyond
the setting of testing exchangeable hypotheses. Under the standard two-groups
model and the Oracle condition, we show that the Bayesian and the frequentist
methods can achieve asymptotically equivalent FDR control at arbitrary levels.
Built on this result, we further illustrate that rigorous post-fitting model
diagnosis is necessary and effective to ensure robust FDR controls for
parametric Bayesian approaches. Additionally, we show that the Bayesian FDR
control approaches are coherent and naturally extended to the setting beyond
testing exchangeable hypotheses. Particularly, we illustrate that $p$-values
are no longer the natural statistical instruments for optimal frequentist FDR
control in testing non-exchangeable hypotheses. Finally, we illustrate that
simple numerical recipes motivated by our theoretical results can be effective
in examining some key model assumptions commonly assumed in both Bayesian and
frequentist procedures (e.g., zero assumption).
