Next, we evaluated the effect of adding DSs on the performance of Gibbs sampling with and without positional clustering. Addition of DSs dilutes enrichment of the TF-binding site in the input set, making motif detection more challenging (17, 22) . Modeling DSs, we repeated our estimate of PPV of TFBS detection with the addition of 1-50 random yeast promoters (DSs) to the original set of 51 STE12-bound promoters. We found that positional clustering improves the PPV of Gibbs sampling by >20% through the addition of up to 80% noise or 40 DSs (Figure 2, Supplementary Figure S3 ). Additionally, results of Gibbs sampling both with and without positional clustering decay linearly with the addition of decoys [R 2 ¼ 0.81 and 0.95, respectively (Supplementary Figure S4) ]. Extrapolating, we predict positional clustering will maintain an improved PPV through the addition of >100% noise or 70 DSs.