Often we will wish to specify nonconjugate priors, for increased flexibility. For example, in the inbreeding single f model, prior information may exist on the coefficient f for which, recall, fmin ≤ f ≤ 1, where fmin=−pmin1−pmin. We require a joint prior for p,f and we assume π(p,f) = π(p) × π(f|p), with an N(μλ,σλ2) prior for λ=log(f−fmin1−f), which gives (9)πf(f∣p)=(2πσλ2)−1∕2exp[−12σλ2{log(f−fmin1−f)−μλ}2]×1−fmin(f−fmin)(1−f), as a prior for f, where the final term corresponds to the Jacobian |dλ/df| (see Appendix). For prior specification we choose two probabilities, along with their corresponding quantiles, for f, and then solve for μλ , σλ. Much data are available on the possible sizes of f. For example, Table 7.3 of Cavalli-Sforza and Bodmer (1971) gives estimates of f for a range of human populations. It is possible that f < 0, for example, due to avoidance of mating relatives, and through selection for heterozygozity.
