We have developed a new algorithm that seeks to improve imputation accuracy at untyped SNPs by improving phasing accuracy at typed SNPs, building on the points raised above. Most HMM-based imputation methods simultaneously estimate missing genotypes and analytically integrate over the unknown phase of SNPs in T. By contrast, we propose to alternately estimate haplotypes at SNPs in T and impute alleles at SNPs in U, assuming the haplotype guesses are correct. We account for the phasing uncertainty in the data by iterating these steps in a Markov chain Monte Carlo (MCMC) framework. Separating the phasing and imputation steps allows us to focus more computational effort on phasing and use more of the available information; the extra computation used in this step is largely balanced by the quick haploid imputation in the step that follows.
