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Chunk #29 — 4. Examples — 4.1 Four Group Data

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Bayesian methods for examining Hardy-Weinberg equilibrium.
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Figure 2 gives prior (top row) and posterior (bottom row) distributions from the single f model. We provide the prior/posterior for f and the single allele frequency p1 (for illustration). Under the single f model Pr(f < 0 | n) = 0.994. The MLE is indicated as the cross on the scatterplot in panel (f). The MLE f^ for the single f model lies on the lower boundary of its range, which led to instability in attempting to derive a standard error. Figure 2f illustrates this problem with the posterior density concentrated near the boundary. When a parameter lies close to its boundary, it is often indicative of model inadequacy and here we interpret f close to its boundary as reflecting an inadequacy of the single f model. Examination of posterior interval estimates under the general fixation model is revealing in this respect.