Pedigree likelihood

For latent genotypes $G_i$ and observed phenotypes $X_i$, assume conditional phenotype independence, independent founder genotypes, and conditionally independent Mendelian transmissions. The likelihood function isThis follows by the chain rule applied to the acyclic ancestry graph, then the law of total probability over all latent genotypes. Penetrance supplies the phenotype factors and genetic recombination supplies multilocus transmission factors.