Probabilistic forecasting

Probabilistic forecasting summarizes what is known about, or opinions about, future events. In contrast to single-valued forecasts (such as forecasting that the maximum temperature at given site on a given day will be 23 degrees Celsius, or that the result in a given football match will be a no-score draw), probabilistic forecasts assign a probability to each of a number of different outcomes, and the complete set of probabilities represents a probability forecast. Thus, probabilistic forecasting is a type of probabilistic classification.

Weather forecasting represents a service in which probability forecasts are sometimes published for public consumption, although it may also be used by weather forecasters as the basis of a simpler type of forecast. For example forecasters may combine their own experience together with computer-generated probability forecasts to construct a forecast of the type "we expect heavy rainfall".

Sports betting is another field of application where probabilistic forecasting can play a role. The pre-race odds published for a horse race can be considered to correspond to a summary of bettors' opinions about the likely outcome of a race, although this needs to be tempered with caution as bookmakers' profits needs to be taken into account. In sports betting, probability forecasts may not be published as such, but may underlie bookmakers' activities in setting pay-off rates, etc..

Probabilistic forecasting is used in a weather forecasting in a number of ways. One of the simplest is the publication of about rainfall in the form of a probability of precipitation.

The probability information is typically derived by using several numerical model runs, with slightly varying initial conditions. This technique is usually referred to as ensemble forecasting by an Ensemble Prediction System (EPS). EPS does not produce a full forecast probability distribution over all possible events, and it is possible to use purely statistical or hybrid statistical/numerical methods to do this. For example, temperature can take on a theoretically infinite number of possible values (events); a statistical method would produce a distribution assigning a probability value to every possible temperature. Implausibly high or low temperatures would then have close to zero probability values.

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