The empirical probability, also known as relative frequency, or experimental probability, is the ratio of the number of outcomes in which a specified event occurs to the total number of trials, not in a theoretical sample space but in an actual experiment. In a more general sense, empirical probability estimates probabilities from experience and observation.
In statistical terms, the empirical probability is an estimate or estimator of a probability. In simple cases, where the result of a trial only determines whether or not the specified event has occurred, modelling using a binomial distribution might be appropriate and then the empirical estimate is the maximum likelihood estimate. It is the Bayesian estimate for the same case if certain assumptions are made for the prior distribution of the probability. If a trial yields more information, the empirical probability can be improved on by adopting further assumptions in the form of a statistical model: if such a model is fitted, it can be used to derive an estimate of the probability of the specified event.
Other articles related to "empirical probability, probability":
... The phrase a-posteriori probability is also used as an alternative to empirical probability or relative frequency ... to Bayesian inference, where a-posteriori probability is occasionally used to refer to posterior probability, which is different even though it has a confusingly similar ... The term a-posteriori probability, in its meaning as equivalent to empirical probability, may be used in conjunction with a priori probability which represents a estimate of a ...
Famous quotes containing the words probability and/or empirical:
“Liberty is a blessing so inestimable, that, wherever there appears any probability of recovering it, a nation may willingly run many hazards, and ought not even to repine at the greatest effusion of blood or dissipation of treasure.”
—David Hume (17111776)
“To develop an empiricist account of science is to depict it as involving a search for truth only about the empirical world, about what is actual and observable.... It must involve throughout a resolute rejection of the demand for an explanation of the regularities in the observable course of nature, by means of truths concerning a reality beyond what is actual and observable, as a demand which plays no role in the scientific enterprise.”
—Bas Van Fraassen (b. 1941)