Table 5 . Posterior probabilities of the IBD state s_iℓ at a single locus ℓ of an individual i.

Observed genotype	IBD state	Posterior probability
wiℓ	siℓ	ℙ(siℓ|wiℓ,Ψ)
AℓkAℓh	1	0
	0	1
AℓkAℓk	1	$\frac{\rho \left(1+{\gamma }_{i\ell }\right)}{\rho \left(1+{\gamma }_{i\ell }\right)+\left(1-\rho \right)\left(2{\gamma }_{i\ell }-{\phi }_{\ell k}{\gamma }_{i\ell }+{\phi }_{\ell k}\right)}$
	0	$\frac{\left(1-\rho \right)\left(2{\gamma }_{i\ell }-{\phi }_{\ell k}{\gamma }_{i\ell }+{\phi }_{\ell k}\right)}{\rho \left(1+{\gamma }_{i\ell }\right)+\left(1-\rho \right)\left(2{\gamma }_{i\ell }-{\phi }_{\ell k}{\gamma }_{i\ell }+{\phi }_{\ell k}\right)}$
XX	1	ρ
	0	1 − ρ

The calculation of ℙ(s_iℓ | w_iℓ, Ψ) is based on Equation 11. h ≠ k.