The huge number of signals that are screened in order to substantiate some claims about a few ones, have made this area of research very receptive to the concern towards selective inference. Still, inference in the form of confidence intervals is rarely appropriately addressed.
Moreover, structured larger problems give rise to new questions regarding the appropriate ways to conduct selective inference. As an important example the complexity of brain structure makes the study of GWAS of brain characteristics especially challenging. The hierarchical FDR testing of multiple families has been developed and used for the above purpose.
As a result of these and other difficulties, the GWAS research community have emphasized the importance of replicating experiments, either fully or only for the promising signals, in order to offer support for discoveries. Still, the usual analysis of replicated experiments does not offer the right support for replicability claims. For various designs we offer such support from various points of view: For full replication studies, both from the frequentist framework and from the Bayesian one; and for a primary study and its partial follow-up study in the frequentist framework. We further propose for that purpose the use of a r-value, being the lowest level of FDR at which a discovery can be among the replicated ones.