 Phase averaging in a linkage likelihood

An unphased multilocus genotype can have several pairs of haplotypes. Its pedigree likelihood must average over these possible phases with prior weights ${\pi }_s$, rather than maximize over phases after observing the offspring. Under linkage disequilibrium, the weights need not be equal. They can be obtained by conditioning population haplotype frequencies on the observed parental genotype; different choices of what is conditioned on change only parameter-independent factors when those frequencies are held fixed.