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Chunk #27 — 4. Examples — 4.1 Four Group Data

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Bayesian methods for examining Hardy-Weinberg equilibrium.
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For these data we fit the HWE (recessive) model, along with the single f and saturated models. For the HWE and saturated models we assume conjugate Dirichlet priors with all parameters set to 1. This prior is flat over the simplex of probabilities, but is far from uninformative on each of the fixation indices. Figure 1a gives the marginal prior density for a generic fixation index; the prior probability that this fixation index is greater than 0 is 0.64. For the single f model we assume the transformed normal prior model described in Section 3.1, and fix prior probabilities Pr(f < 0) = 0.5 and Pr(f < 0.26) = 0.95 to give μλ = −2.95, σλ = 1.07. The normalizing constants for the recessive and saturated models are given by equations (6) and (7) and are 1.39 × 10−11 and 1.88 × 10−10, respectively, to give a Bayes factor of 0.074. Hence the data are 14 times more likely under the saturated model. The probability of the data under the single f model is 1.36 × 10−10 so that the