We refer to this approximation as informed selection of conditioning states. While this method is built upon genealogical intuitions, we emphasize that no explicit genealogies are constructed in our inference scheme. One way of understanding our approach is by comparison to the phasing method of Kong et al. [19]. Their method uses rule-based techniques to phase putative “unrelateds” by identifying long stretches of identity-by-state (IBS) sharing between individuals, under the assumption that such sharing is caused by recent common descent. Our Hamming distance metric can be viewed as a way of identifying near-IBS sharing, and our method combines information across multiple closely related individuals in a model-based way rather than seeking perfect IBS matching between specific individuals. In this sense, our approximation can be viewed as a flexible middle ground between full conditional modeling (which uses all of the available haplotypes to phase an individual) and the Kong et al. method (which may use only a small fraction of the available haplotypes to phase an individual).
