La Score de Brier is a statistical measure used to assess the accuracy of prédictions probabilistes. It is particularly useful in fields such as meteorology, apprentissage automatique, 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 valeur numérique that reflects how well the predicted probabilities correspond to the actual results.
Mathématiquement, le score de Brier est défini comme :
Brier Score = (1/N) * Σ (f_i – o_i)²
Où :
- N est le nombre total de prédictions.
- f_i represents the predicted probability que l'événement se produise.
- o_i est le résultat réel (1 si l'événement s'est produit, 0 sinon).
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 régression logistique et divers classificateurs d'apprentissage automatique.