  In genome-wide association studies (GWAS), hundreds of thousands of genetic
markers (SNPs) are tested for association with a trait or phenotype. Reported
effects tend to be larger in magnitude than the true effects of these markers,
the so-called ``winner's curse.'' We argue that the classical definition of
unbiasedness is not useful in this context and propose to use a different
definition of unbiasedness that is a property of the estimator we advocate. We
suggest an integrated approach to the estimation of the SNP effects and to the
prediction of trait values, treating SNP effects as random instead of fixed
effects. Statistical methods traditionally used in the prediction of trait
values in the genetics of livestock, which predates the availability of SNP
data, can be applied to analysis of GWAS, giving better estimates of the SNP
effects and predictions of phenotypic and genetic values in individuals.
