Brier Score

brier_score(
    observations: ArrayLike,
    forecasts: ArrayLike,
    /,
    *,
    backend: Backend = None,
) -> Array

Compute the Brier Score (BS).

The BS is formulated as

\[ BS(f, y) = (f - y)^2, \]

where \(f \in [0, 1]\) is the predicted probability of an event and \(y \in \{0, 1\}\) the actual outcome.

Parameters:

Name	Type	Description	Default
`observations`	`ArrayLike`	Observed outcome, either 0 or 1.	required
`forecasts`	`NDArray`	Forecasted probabilities between 0 and 1.	required
`backend`	`Backend`	The name of the backend used for computations. Defaults to 'numpy'.	`None`

Returns:

Name	Type	Description
`brier_score`	`NDArray`	The computed Brier Score.