# Error metrics

## Root Mean Squared error

A typical way of measuring the difference between observations and results from a predictor.

The formal definition is:

\begin{aligned} RMSE(\hat{\theta}) &= \sqrt{\operatorname{MSE}(\hat{\theta})} \\ &= \sqrt{\operatorname{E}((\hat{\theta}-\theta)^2)}. \end{aligned}

For $$N$$ observations $$Y=\{y_1,\dots,y_N\}$$ we can express it as:

$RMSE=\sqrt{\frac{\sum_{n=1}^{N}({\hat {y}}_{n}-y_{n})^{2}}{N}}.$