# Empirical Probability

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.