Topic summary
Empirical probability
In probability theory and statistics, the empirical probability or experimental probability of an event is an estimate of the probability of the event occurring. A common estimator for the empirical probability is the relative frequency, calculated as the ratio of the number of recorded event outcomes to the total number of trials. It is produced by means not of a theoretical sample space but of an empirical sample. More generally, empirical probability may be estimated from experience and observation.
Mathematically, given an event A in a sample space, the relative frequency of A is the ratio m being the number of outcomes in which the event A occurs, and n being the total number of outcomes of the experiment.
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