Possible Change

The information contained in this page is a DRAFT under consideration for inclusion in the official BIF Guidelines. It should not be considered to be part of the Guidelines until this message has been removed

Organizations involved in producing EPDs will often provide a table of "possible change" values. Possible change is a measure of the potential difference between an EPD and the true progeny difference, and should be constructed for each trait EPD.

When calculating the possible change table values, inbreeding is assumed to be zero. The relationship between possible change and BIF Accuracy is,

$a_{BIF}=1-{\sqrt {\frac {\sigma _{PE}^{2}}{\sigma _{u}^{2}}}}$

${\sqrt {\frac {\sigma _{PE}^{2}}{\sigma _{u}^{2}}}}=1-a_{BIF}$

${\frac {\sigma _{PE}^{2}}{\sigma _{u}^{2}}}=(1-a_{BIF})^{2}$

$\sigma _{PE}^{2}=(1-a_{BIF})^{2}\sigma _{u}^{2}$

$\sigma _{PE}=(1-a_{BIF})\sigma _{u}$

where $a_{BIF}$ is the BIF Accuracy; $\sigma _{u}^{2}$ is the additive genetic variance of the trait for which the possible change values are being calculated; and $\sigma _{PE}^{2}$ is the prediction error variance. The $\sigma _{PE}$ is the standard error of prediction for an estimated breeding value.

A possible change for an EPD is then calculated as,

$\sigma _{PC}={\frac {\sigma _{PE}}{2}}={\frac {(1-a_{BIF})\sigma _{u}}{2}}$

The defacto standard for possible change is to publish it as being one prediction error standard deviation (square root of the prediction error variance) at each tenth of a BIF accuracy value. Thus, the true value should fall within the range of plus or minus one possible change from the EPD 68% of the time for a given level of BIF Accuracy. It will fall within plus or minus two possible changes from the EPD 95% of the time, etc.

Recommendations

BIF recommends that possible change be published as one standard error of prediction of EPDs.