scoring rules for a continuous variable I was wondering how I can use scoring rules based on accuracy of predicting a continuous  variable, rather than reported probability of different mutually exclusive events. For example, I want to predict tomorrow's temperature in London. There are three forecasters who predict 22, 30, 35 degree. Later, we know the correct outcome is 29 degree. How I can score them ( for example between 0 and 1) based on their prediction error. 
I appreciate your help.
 A: If the forecasting scheme provides point forecast, you can use either Mean Absolute Error (MAE) or Mean Square Error:
$$\text{MAE}_h=\frac{1}{n}\sum_{i=1}^{n} |e_{h}|$$
$$\text{MSE}_h=\frac{1}{n}\sum_{i=1}^{n} (e_{h})^{2}$$
in which $e_{h}$ is the $h$ period ahead forecast error. i.e. the difference between the realized value (Y_h) and the point forecast (F_h):
$$e_h=Y_h-F_h$$
 Note that such measure are size dependent and you might want to use Mean Absolute Percentage Error:
$$\text{MAPE}_h=\frac{1}{n}\sum_{i=1}^{n} |e_{h}/Y_{h}|$$
However, if the forecast scheme generates a probabilistic forecast, in other words, a distribution for all possible outcomes, you have other choices: probabilistic score rules. In the following Q is the forecast with q(.) as its probability mass or density function
A Linear score rule (improper and therefore not recommended): $$S(Q,Y_h)=q(Y_h)$$ 
A logarithmic score rule: $$S(Q,Y_h)=-log(q(Y_h))$$ 
A Quadratic score rule: $$S(Q,Y_h)=-2q(Y_h)+\int_{\mathbb{R}}q(z)^2dz$$
Need more information? I recommend the following sources:
Gneiting, T. and Katzfuss, M. (2014). Probabilistic forecasting. Annual Review of Statistics and Its Application, 3:347–373.
Makridakis, S. G., Wheelwright, S. C., and Hyndman, R. J. (1998). Forecasting: Methods and Applications. John Wiley & Sons, 3rd edition.
