Best Linear Unbiased Prediction

Best linear unbiased prediction (BLUP) describes properties of the mixed-model equations used for national cattle evaluation. Solutions to the mixed-model equations are best, in that they minimize differences between observed performance and performance predicted by linear combinations of factors affecting performance and the solved effects of those factors. The solutions are unbiased with respect to the available data, so that the expected difference between predicted effects and unknown true effect is zero. This does not mean that once a BLUP EPD is predicted for an animal, that EPD will never get better. More data, particularly progeny performance, will result in a better, more accurate EPD than the best EPD predicted before progeny were recorded. This also does not mean that unbiased BLUP can overcome biases that may exist in the data, statistical model, and simplifying assumptions used to predict BLUP EPD.