Our second example was also analyzed by Guo and Thompson (1992) and consists of rhesus data on 8297 individuals with nine groups. The (exact) p-value for these data is 0.71. Under the HWE null we assume the Dirichlet prior with w = (1, 1, 1, 1, 1, 1, 1, 1, 1) so that this prior is uniform on the simplex of allele frequencies. Under the single f alternative we use the information in Table 7.3 of Cavalli-Sforza and Bodmer (1971), which contains estimates of f that are predominantly less than 0.03. Consequently, under the single f model we assume a prior on f that has 50% and 95% points of 0 and 0.03. We obtain normalizing constants for the HWE and the single f model 1.3 × 10−53 and 5.1 × 10−54 so that the data are 2.5 times more likely under the HWE model, as compared to the single f model. For these data, sampling from the prior was not feasible, so instead importance sampling Monte Carlo was implemented using a nine-dimensional normal distributed with moments estimated from an
