To reduce the computational cost, we consider discrete values of α ∈ {α1, ⋯ , αM}, (e.g. 5 – 50% by 5%). We determine that it is a doublet between samples s1, s2 if and only if maxs1,s2,αLc(s1,s2,α)maxsLc(s)≥t and the most likely mixing proportion is estimated to be argmaxαLc(s1, s2, α). We determine that the cell contains only a single individual s if maxs1,s2,αLc(s1,s2,α)maxsLc(s)≤1t, and less confident droplets are classified as ambiguous. While we consider only doublets for estimating doublet rates, we remove all doublets and ambiguous droplets to conservatively estimate singlets. Supplementary Fig. 8 illustrates the distribution of singlet, doublet likelihoods and the decision boundaries when t = 2 was used.
