is the Jacobian for the transformation from (p, f) → (θ, λ). Details are contained in the Appendix. For small numbers of alleles, we sample directly from the prior as in (10), which is a computationally simple approach (because the estimator is simply the likelihood averaged with respect to the prior). This strategy is computationally expensive if either the number of alleles or the sample size is large, however, because the likelihood will be relatively peaked and so the majority of the points will provide essentially zero contribution. As an alternative we may take g(·, ·) in equation (11) as a k-dimensional normal distribution. We run an MCMC sampler (coded in the WinBUGS software, Spiegelhalter, Thomas, and Best, 1998) and take the posterior mean vector and the posterior variance–covariance matrix of (θ, λ) as the moments of g(·, ·).
