Table 3 Regression model performance metrics for predicted (pred) compared to observed (obs) relative damage

Mean Squared Error (MSE)

\({\text{MSE}}= \frac{1}{n}\sum_{i=1}^{n}(pred-obs{)}^{2}\)

Mean Absolute Error (MAE)

\({\text{MAE}}= \frac{1}{n}\sum_{i=1}^{n}pred-obs\)

Mean Bias Error (MBE)

\({\text{MBE}}= \frac{1}{n}\sum_{i=1}^{n}(pred-obs)\)

Quantile Range (QR)

\({\text{QR}}= \frac{1}{n}\sum_{i=1}^{n}{(pred}_{{q95}_{i}}-{pred}_{{q5}_{i}})/{pred}_{{q50}_{i}}\)

Hit Rate (HR)

\({\text{HR}}= \frac{1}{n}\sum_{i=1}^{n}{h}_{i} ;h= \left\{\begin{array}{c}\begin{array}{l}1\quad \text{where pred}_{{q5}_{i}} \le {obs}_{i}\le {pred}_{{q95}_{i}}\\ 0\quad otherwise \end{array}\\ \end{array}\right.\)