Mean Bias Error (MBE)

1. Definition #

$$ \mathrm{MBE} = \frac{1}{n} \sum_{i=1}^n (\hat{y}_i - y_i) $$

• Positive MBE: the model overestimates on average.
• Negative MBE: the model underestimates on average.
• MBE ≈ 0: under- and over-predictions are balanced.

2. Computing in Python #

import numpy as np

def mbe(y_true: np.ndarray, y_pred: np.ndarray) -> float:
    """Mean Bias Error (MBE)."""
    return float(np.mean(y_pred - y_true))

print(f"MBE: {mbe(y_test, y_pred):.3f}")

MBE is easy to implement—it’s simply the mean difference.
Its unit is the same as the target variable.

3. Interpretation Tips #

• A near-zero MBE with large MAE means that positive and negative errors cancel out, even if the model is inaccurate.
• A strongly biased MBE indicates systematic under- or overestimation; bias correction may be needed.
• Also known as Mean Error (ME), it’s widely used in meteorology and energy forecasting.

4. Practical Applications #

• Demand forecasting: A negative MBE implies consistent underestimation, increasing stock-out risk. Use as input for correction factors.
• Energy load prediction: Detect systematic drift in generation or demand forecasts to trigger retraining or feature revision.
• Model comparison: Between models with similar MAE, prefer the one with smaller MBE for lower bias.

5. Comparison with Other Metrics #

Summary #

• MBE is a simple metric to quantify systematic prediction bias.
• Use alongside MAE or RMSE to analyze both bias and accuracy.
• In business contexts, it’s intuitive — e.g., “on average +3 liters overpredicted” — making it easy to communicate with stakeholders.