Das Brier-Score is a statistical measure used to assess the accuracy of probabilistische Vorhersagen. It is particularly useful in fields such as meteorology, maschinellem Lernen, and any domain where predictions involve probabilities. The score is calculated as the mean squared difference between predicted probabilities and the actual outcomes, which are typically binary (0 or 1). This method provides a clear numerischen Wert that reflects how well the predicted probabilities correspond to the actual results.
Mathematisch wird der Brier-Score definiert als:
Brier Score = (1/N) * Σ (f_i – o_i)²
Wo:
- N ist die Gesamtzahl der Vorhersagen.
- f_i represents the predicted probability des Eintretens des Ereignisses dar.
- o_i ist das tatsächliche Ergebnis (1, wenn das Ereignis eingetreten ist, 0, wenn nicht).
The resulting score ranges from 0 to 1, where a Brier Score of 0 indicates perfect accuracy (all predictions are correct), while a score of 1 indicates complete inaccuracy (all predictions are wrong). One of the strengths of the Brier Score is its sensitivity to both the calibration (how well the predicted probabilities reflect the actual outcomes) and the refinement (how close the predicted probabilities are to the actual outcomes).
In practice, lower Brier Scores are preferred, as they indicate better predictive performance. This metric is particularly useful for evaluating models that produce probabilities, such as logistische Regression und verschiedene maschinelle Lernklassifikatoren.