This paper proposes the Bayesian approach as a conceptual strategy to solve problems arising in animal breeding theory. General elements of Bayesian inference, e.g., prior and posterior distributions, informative vs noninformative priors, likelihood functions, finite samples, "memory" properties and integration of nuisance parameters are illustrated with animal breeding examples. Shrinkage estimators are discussed from a Bayesian viewpoint. A general framework for estimation of breeding value with or without selection or assortative mating, including the situation where variances and covariances are unknown, is presented. Selection indexes, best linear unbiased prediction, nonlinear merit functions, nonlinear models and estimation of genetic parameters are discussed from a Bayesian perspective.
Gianola, D., & Fernando, R. L. (1986). Bayesian Methods in Animal Breeding Theory. Journal of Animal Science, 63(1), 217–244. https://doi.org/10.2527/jas1986.631217x