Given a vector of χ2 statistics and LD information either from the sample or from a reference panel, Equation (3) allows us to obtain estimates τ̂c of τc by computing ℓ(j, c) and regressing χ2j on ℓ(j, c). For some analyses—including the cell-type and cell-type group analyses in this manuscript—estimating τc is the goal. For other analyses—including the baseline analyses in this manuscript—the goal is to estimate h2(Cc):=∑j∈Ccβj2, or h2(Cc)/h2. Because the βj have mean zero, we can approximate h2(Cc) with its expectation, Σj∈Cc Var(βj). When the categories are disjoint, Var(βj) = τc, where SNP j is in category Cc, and so ĥ2(Cc) = |Cc|·τ̂c. When the categories overlap, we apply Equation (2), which gives us
