Measure to compare true observed labels with predicted probabilities in multiclass classification tasks.

## Arguments

- truth
(

`factor()`

)

True (observed) labels. Must have the same levels and length as`response`

.- prob
(

`matrix()`

)

Matrix of predicted probabilities, each column is a vector of probabilities for a specific class label. Columns must be named with levels of`truth`

.- ...
(

`any`

)

Additional arguments. Currently ignored.

## Details

Brier score for multi-class classification problems with \(r\) labels defined as $$ \frac{1}{n} \sum_{i=1}^n \sum_{j=1}^r (I_{ij} - p_{ij})^2. $$ \(I_{ij}\) is 1 if observation \(i\) has true label \(j\), and 0 otherwise.

Note that there also is the more common definition of the Brier score for binary
classification problems in `bbrier()`

.

## References

Brier GW (1950).
“Verification of forecasts expressed in terms of probability.”
*Monthly Weather Review*, **78**(1), 1--3.
doi:10.1175/1520-0493(1950)078<0001:vofeit>2.0.co;2
.