The Bayesian approach to hypothesis testing requires consideration of the Bayes factor (Kass and Raftery, 1995), which is the probability of the data under the null divided by the probability of the data under the alternative. In the HWE context the Bayes factor (BF) is given by (4)BF=Pr(n∣H0)Pr(n∣H1)=∫Pr(n∣θ)π(θ)dθ∫∫Pr(n∣θ,λ)π(θ,λ)dθdλ, where θ represent a vector of parameters under the null and λ an additional set of parameters under the alternative hypothesis, with prior distribution π(θ) under the null and joint prior π(θ, λ) under the alternative. A conjugate choice for the parameters under both the null and saturated hypotheses is the Dirichlet distribution. In the k allele case, for the saturated model, let Dir(v) with v = (v11, v12 , . . . , vkk) denote the Dirichlet distribution with parameters v and density: π(p)=Γ(∑i,j=1,j≥ikvij)∏i,j=1,j≥ikΓ(vij)∏i,j=1,j≥ikpijvij−1, where pij > 0 and ∑i,j=1,j≥ikpij=1. Combining this prior on genotype frequencies with the multinomial likelihood gives the Dirichlet posterior Dir(v + n), in an obvious notation. The conjugate prior under the null, Dir(w) with w = (w1 , . . . wk) follows in an analogous
