Chunk #20 — 2 Model — 2.3 Marginal likelihood for γ — 2.3.2 Reducing the complexity from O(m3) to O(k3) — Option 2

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FINEMAP: efficient variable selection using summary data from genome-wide association studies.

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Using properties of the multivariate Normal distribution, the conditional expectation and covariance matrix of zˆN given zˆC are readily available E[zˆN|zˆC]=RNCRCC−1zˆC V[zˆN|zˆC]=RNN−RNCRCC−1RCN and do not depend on Σγ. We rewrite the marginal likelihood p(y|γ,X)=N(zˆ|0,R+RΣγR) in terms of the marginal distribution of zˆC and conditional distribution of zˆN given zˆC to obtain the following expression