El Puntuación de Brier is a statistical measure used to assess the accuracy of predicciones probabilísticas. It is particularly useful in fields such as meteorology, aprendizaje automático, 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 valor numérico that reflects how well the predicted probabilities correspond to the actual results.
Matemáticamente, la puntuación de Brier se define como:
Brier Score = (1/N) * Σ (f_i – o_i)²
Donde:
- N es el número total de predicciones.
- f_i represents the predicted probability de que ocurra el evento.
- o_i es el resultado real (1 si ocurrió el evento, 0 si no).
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 regresión logística y varios clasificadores de aprendizaje automático.