# Accuracy

Information used to calculate EPDs for a particular animal can include pedigree information, own performance data, genomic data, and information on descendants for the trait of interest and correlated traits. Accuracy is dependent upon the value (amount and quality) of the information used for EPD calculation. Beef cattle EPDs in the United States report the BIF Accuracy along with EPDs. However, in theoretical animal breeding and in genetic evaluations in many other countries and species, a different measure of accuracy, the correlation between the estimated breeding value (EBV) and the true breeding value (BV), is used. Therefore, it is important to be aware of the difference.

### BIF Accuracy

BIF accuracy was developed to facilitate users' understanding and utilization of prediction accuracy. It is calculated as, $Accuracy_{BIF}=1-\sqrt{\frac{Prediction\,Error\,Variance}{Additive\,Genetic\,Variance}}$

### Accuracy and reliability

The correlation between EBV and the true BV, $r_{EBV,BV}$ is, $r_{EBV,BV}=\sqrt{1-\frac{Prediction\,Error\,Variance}{Additive\,Genetic\,Variance}}$

Of course, the additive genetic variance in the denominator terms above should be multiplied by one plus the inbreeding coefficient for each animal. The relationship between the two measures of accuracy is, $Accuracy_{BIF}=1-\sqrt{1-r_{EBV,BV}^{2}}$

and, $r_{EBV,BV}=\sqrt{1-\left(1-Accuracy_{BIF}\right)^{2}}$

Theoretically, the prediction error variance is obtained from the inverse of the coefficient matrix of the mixed-model equations. However, in most applications the coefficient matrix is too large to invert and approximations are generally used. The known approximation methods may overestimate the accuracy, especially for young animals and for the contribution made by correlated traits. An alternative that has been implemented is to estimate the prediction error variance from the posterior variance obtained from an MCMC sampler (e.g., Gibb's sampler).