on the multinomial model estimate haplotype frequencies using an expectation-maximization algorithm but can only consider a window of a few markers at a time because haplotype frequencies become too low for accurate estimation otherwise. A third class is explicitly based on population genetics and includes IMPUTE [Marchini et al., 2007] and MACH [Li et al., 2006; Li et al., 2007]. Whereas cluster models are informally based on population genetic principles, IMPUTE is formally based on population genetic parameters in the coalescent framework [Marchini et al., 2007]. IMPUTE conditions imputation on user-supplied reference haplotypes (i.e., IMPUTE does not infer haplotype phase) and a recombination map. MACH can accept either reference genotypes or reference haplotypes and can either continuously update the recombination map and error rates based on the reference panel and study sample together or condition imputation based on maximum-likelihood estimates generated from only the reference panel.
