In Scenario A, IMPUTE v2 estimates marginal posterior probabilities of missing genotypes by alternately phasing all of the SNPs in T in the study sample (simultaneously imputing any sporadically missing genotypes) and then imputing study genotypes at the SNPs in U, conditional on the haplotype guesses from the first step. To explain this process in more detail, we begin by defining , the set of known reference haplotypes at SNPs in T and U (i.e., the entire reference panel); , the set of known reference haplotypes at SNPs in T; and , the set of unobserved study haplotypes at SNPs in T. If there are NS individuals in the study sample, their haplotypes at SNPs in T can be represented as , where is the haplotype pair for study individual i.
