Eagle is a very different method from the “pure” LRP approach of Kong et al.13: in order to create an algorithm that could harness limited, often distant relatedness, we needed to combine aspects of LRP and conventional HMM-based phasing, confirming the hypothesis that “IBD-based phasing can be extended...by using more sensitive methods for detecting IBD and combining IBD-based phasing with population haplotype frequency models”1. Indeed, these ideas have implicitly begun to converge within sophisticated HMM-based methods (e.g., SHAPEIT2), as has recently been observed29. SHAPEIT2 takes a “bottom-up” approach in which it steadily improves phase accuracy over the course of a few dozen MCMC sampling iterations, iteratively copying phase information from progressively more accurate sets of best reference haplotypes. This procedure eventually achieves high-accuracy phase for a proband's (distant) relatives, selects them as reference haplotypes, and uses them to phase the proband29. In contrast, Eagle takes a “top-down” approach, first scanning all pairs of individuals for long IBD tracts and using them to phase long stretches of genome, and then applying only two iterations of approximate HMM decoding to correct errors
