On a misconception about irreducibility of the single-site Gibbs sampler in a pedigree application

The analysis of genetic data on groups of related individuals, or pedigrees, frequently necessitates the calculation of probabilities and likelihoods, although, in practice, exact methods break down either when the pedigree structure or the genetic model under consideration becomes too complicated. In these situations, the required probabilities and likelihoods must be estimated, and one approach is to approximate the problem by sacrificing a sufficient amount of the complexity to enable exact calculation.