UK Accounting Glossary

The empirical probability of an event 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.

Empirical Probability is sometimes also referred to as: relative frequency or experimental probability

In probability theory, the **empirical probability** is an *estimated* probability based upon previous evidence or experimental results. As such, the empirical probability is sometimes referred to as **experimental probability**, and we can distinguish it from probabilities calculated from a clearly-defined **sample space**.

The empirical probability, relative frequency, or experimental probability of an event 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, the empirical probability estimates probabilities from observation and experience.

Given an event A in a sample space, the relative frequency of A is the ratio m/n, m being the number of outcomes in which the event A occurs, and n being the total number of outcomes of the experiment.

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.

In order for a theory to be proved or disproved, empirical evidence must be collected. An empirical study will be performed using actual market data. For example, many empirical studies have been conducted on the capital asset pricing model (CAPM), and the results are slightly mixed.

In some analyses, the model does hold in real-world situations, but most studies have disproved the model for projecting returns. Although the model is not completely valid, that is not to say that there is no utility associated with using the CAPM. For instance, the CAPM is often used to estimate a company’s weighted average cost of capital.

The phrase a-posteriori probability is also used as an alternative to empirical probability or relative frequency. The use of the phrase “a-posteriori” is reminiscent of terms in Bayesian statistics, but is not directly related 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 name.

The term a-posteriori probability, in its meaning as equivalent to empirical probability, may be used in conjunction with a priori probability which represents an estimate of a probability not based on any observations but based on deductive reasoning

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Definitions for Empirical Probability are sourced/syndicated and enhanced from:

**A Dictionary of Economics (Oxford Quick Reference)****BusinessDictionary.com****Oxford Dictionary Of Accounting****Oxford Dictionary Of Business & Management**

This glossary post was last updated: 9th August 2019.