In Step 1, the algorithm phases individual i's observed genotype by sampling from . The model we use to specify this conditional distribution is essentially the same one used by IMPUTE v1 [6] – i.e., we use a hidden Markov model that is based on an approximation to the coalescent-with-recombination process [16]. This model views newly sampled haplotypes as “imperfect mosaics” of haplotypes that have already been observed. As with IMPUTE v1, we use an estimated fine-scale recombination map [17] for SNP-to-SNP transition probabilities and a result from population genetics theory [6] for emission probabilities, which model historical mutation.
