For each diploid proband in turn, Eagle identifies candidate surrogate parental haplotypes (from the output of step 2) for use within an HMM (similar to the Li-Stephens model46). Eagle then computes an approximate maximum likelihood path through the HMM using a modified Viterbi algorithm (aggressively pruning the state space to increase speed) and calls phase according to the HMM decoding. Finally, Eagle post-processes the phase calls to correct sporadic errors by explicitly taking into account haplotype frequencies and long IBD. Eagle runs two iterations of this entire procedure. In our N≈150,000 analyses, this step required ≈70% of the total computation time (Supplementary Table 2) and reduced the switch error rate to ≈0.4% after the first HMM iteration and ≈0.3% after the second (Fig. 1c,d). In more detail, our algorithm applies the following three procedures to each proband in turn (in each HMM iteration).
