Yesterday’s question Determine accuracy of model which estimates probability of event got me curious about probability scoring.

The Brier score

$$\frac{1}{N}\sum\limits _{i=1}^{N}(\text{prediction}_i – \text{reference}_i)^2$$

is a mean squared error measure.

Does the analogous mean absolute error performance measure

$$\frac{1}{N}\sum\limits _{i=1}^{N}|\text{prediction}_i – \text{reference}_i|$$

have a name, too?

**Answer**

Answer seems to be: no, because MAE doesn’t lead to a proper scoring rule.

See Loss Functions for Binary Class Probability Estimation and Classification: Structure and Applications where the MAE is discussed under “Counterexamples of proper scoring rules”.

**Attribution***Source : Link , Question Author : cbeleites unhappy with SX , Answer Author : cbeleites unhappy with SX*