We also find that the beta approximation does consistently better than the direct method for the same number of permutations, especially when few permutations are used (50 or 100). As a consequence, using 500 permutations with the beta approximation, for example, has the same accuracy to recover the optimal set as the direct method using 1000 permutations. Interestingly, the beta approximation using only 50/100 permutations already does very well at recovering the optimal eQTL set.
