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Originally published as Genetics Published Articles Ahead of Print on August 24, 2007.

Genetics, Vol. 177, 1255-1258, October 2007, Copyright © 2007
doi:10.1534/genetics.107.077487

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Derivation of the Shrinkage Estimates of Quantitative Trait Locus Effects

Shizhong Xu1

Department of Botany and Plant Sciences, University of California, Riverside, California 92521

1 Address for correspondence: 900 University Ave., University of California, Riverside, CA 92521-0124.
E-mail: xu{at}genetics.ucr.edu

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.






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Copyright © 2007 by the Genetics Society of America.