Scoring rule

In decision theory is a score function, or scoring rule to a German valuation rule, a measure of the performance of an individual, when afflicted decisions with uncertainty. As an example, the weather forecast can be used. Here, a probability of rain for each day is generated. By the statistics of the predictions, the actual frequency of rain can be compared with the prediction. If the forecasts are often wrong, as it is called poorly calibrated. Can Predictive be motivated to improve its performance, then a function can be used when this is the prediction and when it rains, and when not. Will now optimize its performance with this feature of Predictive, then maximize the following function;

Where p is the probability of predicting personal agendas is that it will rain.

Proper score functions

A scoring rule is called proper, so clean, if only depends on the probability of Predictive is so motivated to appreciate honest and coherent. Two of the most commonly used scoring rules are: The Brier score is given by

And the logarithmic score function.

More scoring rules

These are examples of strictly proper scoring rules:

The quadratic score:

The spherical scoring rule: