Pedigree likelihood
= 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> is
$$
\sum_{(G_i)}\prod_i P(X_i\mid G_i)\prod_{i\in F}P(G_i)\prod_{i\notin F}P(G_i\mid G_{m(i)},G_{f(i)}).
$$
This 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.