We begin by describing the basic IMPUTE2 algorithm, which will be retained in this work with some modifications. Full details of the original algorithm are available in Howie et al. (2009). Although that paper addressed the use of multiple reference panels typed on different SNP sets (“Scenario B” in their terminology), for simplicity we will focus on the situation where the reference haplotypes are all defined on the same SNPs (“Scenario A”). Although we do not discuss Scenario B in this paper, the ideas presented here are easily extended to that setting.