Derivation of the shrinkage estimates of quantitative trait locus effects.
The shrinkage estimate of a quantitative trait locus (QTL) effect is the posterior mean of the QTL effect when a normal prior distribution is assigned to the QTL. This note gives the derivation of the shrinkage estimate under the multivariate linear model. An important lemma regarding the posterior mean of a normal likelihood combined with a normal prior is introduced. The lemma is then used to derive the Bayesian shrinkage estimates of the QTL effects.
Xu
Shizhong
S
Department of Botany and Plant Sciences, University of California, Riverside, California 92521, USA. xu@genetics.ucr.edu
D001499:Bayes Theorem; D008962:Models, Theoretical; D016011:Normal Distribution; D040641:Quantitative Trait Loci