Probabilistic forecasting
Encyclopedia
Probabilistic forecasting summarises what is known, or opinions about, future events. In contrast to a 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.
Weather forecasting
represents a service in which probability forecasts are sometimes published for public consumption, although they 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 bookmaker
s' 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 In sports betting, probability forecasts may not be published as such, but may underlie bookmakers' activities in setting pay-off rates, etc..
in a number of ways. One of the simplest is the publication of about rainfall in the form of a probability of precipitation
.
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) from zero to infinity; 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.
If it were possible to run the model for every possible set of initial conditions, each with an associated probability, then according to how many members (i.e., individual model runs) of the ensemble predict a certain event, one could compute the actual conditional probability of the given event. In practice, forecasters try to guess a small number of perturbations (usually around 20) that they deem are most likely to yield distinct weather outcomes. Two common techniques for this purpose are breeding vectors (BV) and singular vectors (SV). This technique is not guaranteed to yield an ensemble distribution identical to the actual forecast distribution, but attaining such probabilistic information is one goal of the choice of initial perturbations. Other variants of ensemble forecasting systems that have no immediate probabilistic interpretation include those that assemble the forecasts produced by different numerical weather prediction
systems.
s such as the continuous-ranked probability score for evaluating probabilistic forecasts. One example of such a rule is the Brier score
.
Weather forecasting
Weather forecasting
Weather forecasting is the application of science and technology to predict the state of the atmosphere for a given location. Human beings have attempted to predict the weather informally for millennia, and formally since the nineteenth century...
represents a service in which probability forecasts are sometimes published for public consumption, although they 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
Sports betting
Sports betting is the activity of predicting sports results and placing a wager on the outcome.-United States of America:Aside from simple wagers such as betting a friend that one's favorite baseball team will win its division or buying a football "square" for the Super Bowl, sports betting is...
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 bookmaker
Bookmaker
A bookmaker, or bookie, is an organization or a person that takes bets on sporting and other events at agreed upon odds.- Range of events :...
s' 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..
Weather forecasting
Probabilistic forecasting is used in a weather forecastingWeather forecasting
Weather forecasting is the application of science and technology to predict the state of the atmosphere for a given location. Human beings have attempted to predict the weather informally for millennia, and formally since the nineteenth century...
in a number of ways. One of the simplest is the publication of about rainfall in the form of a probability of precipitation
Probability of Precipitation
A probability of precipitation is a formal measure of the likelihood of precipitation that is often published from weather forecasting models. Its definition varies.-U.S. usage:...
.
Ensembles
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 forecastingEnsemble forecasting
Ensemble forecasting is a numerical prediction method that is used to attempt to generate a representative sample of the possible future states of a dynamical system...
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) from zero to infinity; 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.
If it were possible to run the model for every possible set of initial conditions, each with an associated probability, then according to how many members (i.e., individual model runs) of the ensemble predict a certain event, one could compute the actual conditional probability of the given event. In practice, forecasters try to guess a small number of perturbations (usually around 20) that they deem are most likely to yield distinct weather outcomes. Two common techniques for this purpose are breeding vectors (BV) and singular vectors (SV). This technique is not guaranteed to yield an ensemble distribution identical to the actual forecast distribution, but attaining such probabilistic information is one goal of the choice of initial perturbations. Other variants of ensemble forecasting systems that have no immediate probabilistic interpretation include those that assemble the forecasts produced by different numerical weather prediction
Numerical weather prediction
Numerical weather prediction uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions. Though first attempted in the 1920s, it was not until the advent of computer simulation in the 1950s that numerical weather predictions produced realistic...
systems.
Examples
Canada has been one of the first countries to broadcast their probabilistic forecast by giving chances of precipitation in percentages. As an example of fully probabilistic forecasts, recently, distribution forecasts of rainfall amounts by purely statistical methods have been developed whose performance is competitive with hybrid EPS/statistical rainfall forecasts of daily rainfall amounts.Energy usage
Lumina Decision Systems has created an example probabilistic forecast of energy usage for the next 25 years using the US Department of Energy's Annual Energy Outlook (AEO) 2010.Population forecasting
Probaility forecasts have also been used in the field of population forecasting.Assessment
Assessing probabilistic forecasts is more complex than assessing deterministic forecasts. If an ensemble-based approach is being used, the individual ensemble members need first to be combined and expressed in terms of a probability distribution. There exist probabilistic (proper) scoring ruleScoring rule
In decision theory a score function, or scoring rule, is a measure of the performance of an entity, be it person or machine, that repeatedly makes decisions under uncertainty. For example, every evening a TV weather forecaster may give the probability of rain on the next day, in a type of...
s such as the continuous-ranked probability score for evaluating probabilistic forecasts. One example of such a rule is the Brier score
Brier score
The Brier score is a proper score function that measures the accuracy of a set of probability assessments. It was proposed by Glenn W. Brier in 1950....
.