The likelihood function p(y|λ,X) of the causal SNP effects is (proportional to) a Normal density N(λˆ|λ,σ2(nR)−1). This enables an analytic solution for the marginal likelihood of γ eliminating the causal effects where we defined Σγ≡nsλ2Δγ. Importantly, an evaluation of the marginal likelihood requires only single-SNP z-scores and SNP correlations from a reference panel and does not depend on σ2. This elimination of λ is similar to the one used by CAVIAR and CAVIARBF and differs from PAINTOR that fixes those values based on the observed z-scores. Next, we describe two implementations to evaluate N(zˆ|0,R+RΣγR) with high computational efficiency.
