An efficient algorithm to compute marginal posterior genotype probabilities for every member of a pedigree with loops

Marginal posterior genotype probabilities need to be computed for genetic analyses such as geneticcounseling in humans and selective breeding in animal and plant species.

In this paper, we describe a peeling based, deterministic, exact algorithm to compute efficiently genotype probabilities for every member of a pedigree with loops without recourse to junction-tree methods from graph theory. The efficiency in computing the likelihood by peeling comes from storing intermediate results in multidimensional tables called cutsets. Computing marginal genotype probabilities for individual i requires recomputing the likelihood for each of the possible genotypes of individual i. This can be done efficiently by storing intermediate results in two types of cutsets called anterior and posterior cutsets and reusing these intermediate results to compute the likelihood.

A small example is used to illustrate the theoretical concepts discussed in this paper, and marginal genotype probabilities are computed at a monogenic disease locus for every member in a real cattle pedigree.