The false discovery rate: a variable selection perspective

In many scientific and medical settings, large-scale experiments are generating large quantities of data that lead to inferential problems involving multiple hypotheses. This has led to recent tremendous interest in statistical methods regarding the false discovery rate (FDR). Several authors have studied the properties involving FDR in a univariate mixture model setting. In this article, we turn the problem on its side; in this manuscript, we show that FDR is a by-product of Bayesian analysis of variable selection problem for a hierarchical linear regression model. This equivalence gives many Bayesian insights as to why FDR is a natural quantity to consider. In addition, we relate the risk properties of FDR-controlling procedures to those from variable selection procedures from a decision theoretic framework different from that considered by other authors.