Each covariance matrix Vj is specified as Vj = SjCSj, where C is a correlation matrix that accounts for correlations among the measurements in the R conditions, and Sj is the R × R diagonal matrix with diagonal elements s^j1,…,s^jR. If measurements in the R conditions are independent, one would set C = IR, the R × R identity matrix, and therefore Vj=Sj2. However, in our GTEx analysis the measurements are correlated due to sample overlap (individuals in common) among tissues; we estimate this correlation from the data (see “Estimating the correlation matrix C” below). The methods place no restriction on the Vj except that they must be symmetric positive definite matrices.
