Past exam of the mathematics course of the University of Cambridge / 2001 / iii / Paper 29 / 6 / iii

For known parental haplotypes, count $r_1$ recombinant transmissions among $m_1$ informative meioses. The conditional pedigree likelihood has the formwhere $C_1$ contains parameter-independent gamete and genotype factors. Differentiating its logarithm gives $r_1/\theta -(m_1-r_1)/(1-\theta )$, so the constrained maximum-likelihood estimate isWhen $r_1=0$ the maximum is at zero; if no meiosis is informative, the likelihood is constant and the parameter is not estimable from that family. This formula presumes the family phase has been resolved; otherwise use phase averaging in a linkage likelihood first.

The family-specific value cannot be calculated because its pedigree, phases and transmission counts are absent from the supplied PDF. The missing data cannot be reconstructed from the requested estimate alone.