Technical note: detection of bias in genetic predictions

The theoretical development of a procedure to detect bias in genetic predictions is presented. The procedure is based on the expectation of three statistics. These statistics detect bias by identifying systematic, unexpected change in subsequent analyses. Expectations of the following statistics were obtained: linear correlation coefficient between subsequent predictions, linear regression of recent (more accurate) on previous (less accurate) genetic prediction, and variance of the genetic prediction difference (recent minus previous genetic prediction). Deviations from these expectations can be used to indicate bias. The covariance between subsequent BLUP of genetic value is shown to equal the variance of the early estimate, implying that the expected value of the regression of recent on previous genetic prediction equals 1 regardless of the distribution of the observations and predictions. Also, the expected value of the linear correlation coefficient between subsequent genetic predictions equals the square root of the ratio of the means of the square of accuracy values. The expected value of the variance of the genetic prediction difference was shown to be equal to the difference between prediction error variances.