For genetic applications we cannot necessarily assume that all our markers are unlinked and thus independent. For instance, in the International Haplotype Map project [26], markers were chosen about 5,000 bases apart (phase 1), or about 1,000 bases apart (phase 2), and so nearby markers will often be in LD. Mathematically this will induce correlation between nearby columns of our matrix M. The effect of this will be that the matrix should be “Wishart-like,” but the nonindependence of the columns will reduce the effective sample size. We will discuss this further (see Correcting for LD) but now introduce a new idea. This adds robustness to our methods, so that minor deviations from the model become of lesser importance.
