Finally, we investigated the speed and accuracy with which Matrix eQTL (direct method) and FastQTL (beta approximation) using 100, 500 and 1000 permutations could reproduce the outcome of the pilot phase of GTEx; a large-scale eQTL mapping study. Of note, we run Matrix eQTL in the most highly effective setting we could achieve in order to fully utilize its matrix based design (Supplementary material 4). Overall, we find that both FastQTL and Matrix eQTL recapitulate the official eQTL set well, especially as the number of permutations increases (Fig. 2e). For the same number of permutations, we find that the closest eQTL set to the official one is consistently provided by FastQTL. Again, it also performs well even when only 100 permutations are used to fit the beta distributions. To process all nine datasets with 1000 permutations, FastQTL requires ∼191 CPU hours which is ∼16 times faster than running the same number of permutations with Matrix eQTL (Table 1). When using only 100 permutations, this is reduced to only ∼33 CPU hours. Table 1.FastQTL and Matrix eQTL running timesNumber of permutationsMatrix