Bayesian approaches have been described by a number of authors. Altham (1971) showed the close link between the exact test and a posterior tail area under a Dirichlet prior, while Pereira and Rogatko (1984) considered the two allele case with estimation and testing via Bayes factors being carried out with Dirichlet priors. Lindley (1988) also considered this case and parameterized in terms of α=12log4p11p22p122 and β=12logp11p22. HWE corresponds to 4p11p22=p122, or equivalently α = 0. When α = 0, β=logp11−p1, where p1 is the frequency of allele A1. An advantage of this parameterization is that α and β are defined over the whole real line, which simplifies inference. A disadvantage is the lack of interpretability of the parameters, which makes prior specification difficult. Shoemaker, Painter, and Weir (1998) considered estimation for the two allele case and placed prior distributions on either the allele frequencies or on the disequilibrium parameter D=p11−p12, which (as with f) is subject to awkward constraints; these authors used numerical integration to obtain the posterior distribution. Ayres and Balding (1998) considered estimation for the fixation indices model,
