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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., Comment: Published in at http://dx.doi.org/10.1214/09-STS306 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org)