graphld.likelihood

Gaussian likelihood functions for GWAS summary statistics under an infinitesimal model.

Model

The likelihood of GWAS summary statistics under an infinitesimal model is:

$\beta \sim N(0, D)$

$z|\beta \sim N(n^{1/2}R\beta, R)$

where:

• $\beta$ is the effect-size vector in s.d-per-s.d. units
• $D$ is a diagonal matrix of per-variant heritabilities
• $z$ is the GWAS summary statistic vector
• $R$ is the LD correlation matrix
• $n$ is the sample size

Precision-Premultiplied Statistics

The likelihood functions operate on precision-premultiplied GWAS summary statistics:

$pz = n^{-1/2} R^{-1}z \sim N(0, M), \quad M = D + n^{-1}R^{-1}$

For model context and practical interpretation, see the Likelihood Functions guide.

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