Analysing the joint association between a large set of responses and predictors is a fundamental statistical task in integrative genomics, exemplified by numerous expression Quantitative Trait Loci (eQTL) studies. Of particular interest are the so-called : hotspots : , important genetic variants that regulate the expression of many genes. Recently, attention has focussed on whether eQTLs are common to several tissues, cell-types or, more generally, conditions or whether they are specific to a particular condition.