We model standardized phenotypes y using the linear model y=∑ixiβi+ϵ, where xi denotes standardized SNP genotypes, βi denotes effect size, and ϵ is a residual term. We use a point-normal model for βi: βi|ai∼{N(0,var[βi|βi≠0])withprobabilityP(βi≠0|ai)0otherwise, where ai are the functional annotations of SNP i, P(βi ≠ 0|ai) is its prior causal probability, and var[βi|βi ≠ 0] is its causal variance, which we assume is independent of ai. This assumption is motivated by our recent work showing that functional enrichment is primarily due to differences in polygenicity rather than differences in effect-size magnitude, which is constrained by negative selection34.
