Assuming independent unlinked loci, the likelihood for the overall genome is then simply the product of the single locus likelihoods. We used the EM algorithm [Dempster et al., 1977] to find maximum-likelihood estimators for the k-coefficients [McPeek and Sun, 2000] and then obtained an estimate of the kinship coefficient ϕ̂ = 0.5k̂2 + 0.25k̂1. The EM algorithm provides more efficient computation than the simplex method, a hill-climbing optimization technique, which has been used previously [Milligan, 2003].
