Table 3 . Posterior joint probabilities of true genotypes g_iℓ and IBD states s_iℓ at a single locus ℓ of an individual i.

Observed genotype	True genotype	IBD state	Joint probability	Posterior probability
wiℓ	giℓ	siℓ	ℙ(giℓ, siℓ, wiℓ|Ψ)	ℙ(giℓ, siℓ|wiℓ, Ψ)
AℓkAℓh	AℓkAℓh	1	0	0
		0	2(1 − ρ)φℓkφℓh(1 − γiℓ)2	1
	Others	1	0	0
		0	0	0
AℓkAℓk	AℓkAℓh	1	0	0
		0	2(1 − ρ)φℓkφℓhγiℓ(1 − γiℓ)	$\frac{2\left(1-\rho \right){\phi }_{\ell h}{\gamma }_{i\ell }}{\rho \left(1+{\gamma }_{i\ell }\right)+\left(1-\rho \right)\left(2{\gamma }_{i\ell }-{\phi }_{\ell k}{\gamma }_{i\ell }+{\phi }_{\ell k}\right)}$
	AℓkAℓk	1	$\rho {\phi }_{\ell k}\left(1-{\gamma }_{i\ell }^2\right)$	$\frac{\rho \left(1+{\gamma }_{i\ell }\right)}{\rho \left(1+{\gamma }_{i\ell }\right)+\left(1-\rho \right)\left(2{\gamma }_{i\ell }-{\phi }_{\ell k}{\gamma }_{i\ell }+{\phi }_{\ell k}\right)}$
		0	$\left(1-\rho \right){\phi }_{\ell k}^2\left(1-{\gamma }_{i\ell }^2\right)$	$\frac{\left(1-\rho \right){\phi }_{\ell k}\left(1+{\gamma }_{i\ell }\right)}{\rho \left(1+{\gamma }_{i\ell }\right)+\left(1-\rho \right)\left(2{\gamma }_{i\ell }-{\phi }_{\ell k}{\gamma }_{i\ell }+{\phi }_{\ell k}\right)}$
XX	AℓkAℓh	1	0	0
		0	$2\left(1-\rho \right){\phi }_{\ell k}{\phi }_{\ell h}{\gamma }_{i\ell }^2$	2(1 − ρ)φℓkφℓh
	AℓkAℓk	1	$\rho {\phi }_{\ell k}{\gamma }_{i\ell }^2$	ρφℓk
		0	$\left(1-\rho \right){\phi }_{\ell k}^2{\gamma }_{i\ell }^2$	$\left(1-\rho \right){\phi }_{\ell k}^2$

The calculation of ℙ(g_iℓ, s_iℓ | w_iℓ, Ψ) is based on Equation 8. h ≠ k.