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Chunk #32 — 4. Examples — 4.2 Nine Group Data

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Bayesian methods for examining Hardy-Weinberg equilibrium.
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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 MCMC run. For illustration, the probability of the data under the saturated model with conjugate Dirichlet prior with a vector of 45 1's is 8.7 × 10−119, emphatically ruling out this model. The “model” being summarized by the normalizing constant consists of the likelihood and the prior, and the conjugate prior assumed here is very unappealing for these data because it gives priors on the fixation indices that are not realistic. Figure 1b gives the induced marginal prior on a generic fixation index and shows that the distribution is not concentrated close to zero as is reasonable in this context.