When GWAS genotypes have been phased prior to imputation, each haplotype can be imputed separately if we assume that the GWAS haplotypes are conditionally independent, given a reference panel. The reference panel provides template haplotypes for the imputation model, and marginal probabilities for the untyped alleles in each GWAS haplotype are estimated via standard hidden Markov model (HMM) calculations (the “forward-backward” algorithm24). The parameters of the HMM are estimated in different ways by minimac and IMPUTE2; see elsewhere for details6,12. Allelic probabilities are converted to genotypic probabilities for each individual by assuming Hardy-Weinberg equilibrium; these genotypic probabilities can be directly compared with those produced by other imputation approaches.
