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Chunk #22 — 3. Bayesian Approaches — 3.2 Estimation

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Bayesian methods for examining Hardy-Weinberg equilibrium.
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Exploitation of conjugate prior distributions allows closed form inference for allele frequencies under HWE, and under the saturated alternative model for the genotype frequencies, but such closed form inference is not available for the fixation indices. However, it is straightforward to obtain samples for these indices, by simple transformation of the samples for p. Specifically, if p(s), s = 1 , . . . , S represent samples from the posterior for the collection of geno-type frequencies, pij, then fij(s)=1−pij(s)∕2pi(s)pj(s) with pi(s)=2pii(s)+∑i,j=1,i≠jkpij(s), pj(s)=2pjj(s)+∑i,j=1,i≠jkpji(s).