The goal of animal breeders is to genetically improve traits of the population by selecting the best candidates as parents of a future generation.
Observed traits are the result of both genetic and environmental effects.
The typical application simoultaneously predicts genetic effects of several thousands to millions of animals using iterative algorithms. BLUP assumes known genetic and residual variances which have to be estimated in practice. Due to the availability of Markov chain Monte Carlo procedures, such as Gibbs sampling, Bayesian estimation is becoming popular also among animal breeders. The computational costs for variance component estimation are high which limits the size of problems that can be handled.