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()`

.

mbrier(truth, prob, ...)

## 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. |

## Value

Performance value as `numeric(1)`

.

## 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
.

## See also

## Examples

#> [1] 1.084326