In other words, based on a strictly proper score rule, a forecasting scheme must score best, if it suggests the target variable as the forecast, and if it scores best, the suggested forecast must be the target variable.
Although scoring rules are introduced in probabilistic forecasting literature, the definition is general enough to consider non-probabilistic measures such as mean absolute error or mean square error as some specific scoring rules.
An example of probabilistic forecasting is in meteorology where a weather forecaster may give the probability of rain on the next day.
If the actual percentage was substantially different from the stated probability we say that the forecaster is poorly calibrated.
A poorly calibrated forecaster might be encouraged to do better by a bonus system. A bonus system designed around a proper scoring rule will incentivize the forecaster to report probabilities equal to his personal beliefs.
The image to the right shows an example of a scoring rule, the logarithmic scoring rule, as a function of the probability reported for the event that actually occurred.
One way to use this rule would be as a cost based on the probability that a forecaster or algorithm assigns, then checking to see which event actually occurs.
If a proper scoring rule is used, then the highest expected reward is obtained by reporting the true probability distribution.
The use of a proper scoring rule encourages the forecaster to be honest to maximize the expected reward. A scoring rule is strictly proper if it is uniquely optimized by the true probabilities.
Optimized in this case will correspond to maximization for the quadratic, spherical, and logarithmic rules but minimization for the Brier Score.
This can be seen in the image at right for the logarithmic rule. Here, Event 1 is expected to occur with probability of 0. The way to maximize the expected reward is to report the actual probability of 0.
This property holds because the logarithmic score is proper. There are an infinite number of scoring rules, including entire parameterized families of proper scoring rules.
The ones shown below are simply popular examples. The logarithmic scoring rule is a local strictly proper scoring rule.
This is also the negative of surprisal , which is commonly used as a scoring criterion in Bayesian Inference ; the goal is to minimize expected surprise.
This scoring rule has strong foundations in information theory. Here, the score is calculated as the logarithm of the probability estimate for the actual outcome.
The goal of a forecaster is to maximize the score and for the score to be as large as possible, and Note that any logarithmic base may be used, since strictly proper scoring rules remain strictly proper under linear transformation.
The Brier score , originally proposed by Glenn W. Brier in ,  can be obtained by an affine transform from the quadratic scoring rule. An important difference between these two rules is that a forecaster should strive to maximize the quadratic score yet minimize the Brier score.
This is due to a negative sign in the linear transformation between them. All proper scoring rules are equal to weighted sums integral with a non-negative weighting functional of the losses in a set of simple two-alternative decision problems that use the probabilistic prediction, each such decision problem having a particular combination of associated cost parameters for false positive and false negative decisions.
Any given proper scoring rule is equal to the expected losses with respect to a particular probability distribution over the decision thresholds; thus the choice of a scoring rule corresponds to an assumption about the probability distribution of decision problems for which the predicted probabilities will ultimately be employed, with for example the quadratic loss or Brier scoring rule corresponding to a uniform probability of the decision threshold being anywhere between zero and one.
Shown below on the left is a graphical comparison of the Logarithmic, Quadratic, and Spherical scoring rules for a binary classification problem.
The x-axis indicates the reported probability for the event that actually occurred. It is important to note that each of the scores have different magnitudes and locations.
The magnitude differences are not relevant however as scores remain proper under affine transformation. A range of Early Warning Scores have been developed in response to the needs of specific patient types e.
A second version of the score was introduced in The revised version was optimised for the identification of sepsis , alternative oxygen targets in people with underlying lung disease, and the onset of delirium.
From Wikipedia, the free encyclopedia. Early warning score Medical diagnostics Purpose determine degree of illness An early warning score EWS is a guide used by medical services to quickly determine the degree of illness of a patient.
Quarterly Journal of Medicine. Critical care London, England. Royal College of Physicians. Acutely ill patients in hospital. Royal College of Physicians of London.
Retrieved from " https: First aid Emergency medicine Intensive care medicine.