The local false sign rate (lfsr) is defined by Stephens16 as: lfsrjr :=min{Pr(bjr≥0 | D),Pr(bjr≤0 | D)}, where D denotes the available data. Intuitively, lfsrjr is the probability that we would incorrectly predict the sign of the effect if we were to use our best guess of the sign (positive or negative). Thus, a small lfsr indicates high confidence in the sign of an effect. The lfsr is more conservative than the local false discovery rate (lfdr)39 because requiring high confidence in the sign is more stringent than requiring high confidence that the effect be non-zero. More importantly, the lfsr is more robust to modelling assumptions than the lfdr16, a particularly important issue in multivariate analyses where modelling assumptions play a larger role.
