The application of Gibbs sampling is considered for inference in a mixed inheritance model in animal populations. Implementation of the Gibbs sampler on scalar components, as used for human populations, appeared not to be efficient, and an approach with blockwise sampling of genotypes was proposed for use in animal populations. The blockwise sampling of genotypes was proposed for use in animal populations. The blockwise sampling by which genotypes of a sire and its final progeny were sampled jointly was effective in improving mixing, although further improvements could be looked for. Posterior densities of parameters were visualised from Gibbs samples; from the former highly marginalised Bayesian point and interval estimates can be obtained.
Janss, L. L. G., Thompson, R., & van Arendonk, J. A. M. (1995). Application of Gibbs sampling for inference in a mixed major gene-polygenic inheritance model in animal populations. Theoretical and Applied Genetics, 91, 1137-1147. https://doi.org/10.1007/BF00223932