In our particular problem, we propose to model the smallest nominal P-value coming from L tests performed in a permutation pass as a beta distributed random variable with shape parameters k = 1 and n = L. However, given that nearby variant sites usually exhibit some relatively high degree of correlation (LD), the L tests performed are not independent, implying that the effective number of tests n is lower than the actual number L of variants in cis. Instead of fixing the k and n parameters a priori, we use a more flexible approach in which the parameters are estimated by maximum likelihood (Galwey, 2009). Specifically, we perform R permutations to generate a null set of P-values {p1, …, pR} and then estimate k and n by maximizing the following log-likelihood: (4)L(k,n|p1,…,pR)=(k−1)∑r=1Rlnpr+(n−1)∑r=1Rln(1−pr)−Rln[Γ(k)Γ(n)Γ(kn)]
