The key quantity that PolyFun uses to estimate prior causal probabilities is the per-SNP heritability of SNP i, var[βi|ai] (we refer to this quantity as per-SNP heritability because the total SNP-heritability var[∑ixiβi|a] is equal to ∑ivar[βi|ai], assuming that causal SNP effects have zero mean and are uncorrelated with other SNP effects and with other SNPs conditional on a). PolyFun relates the prior causal probability P(βi ≠ 0|ai) to the per-SNP heritability var[βi|ai] via the law of total variance: (2)P(βi≠0|ai)=var[βi|ai]var[βi|βi≠0].
