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EMPIRICAL PROBABILITY
This is also known as an experimental probability which can be defined as the e ratio of the number of outcomes in which a specified event occurs to the total number of trials. It is not in a theoretical sample space but in an actual experiment and in a more general sense the empirical probability estimates probabilities from experience as well as the observation.
In statistical terms, this is an estimate or estimator of a probability and in simple cases, the result of a trial determines whether or not the specified event has occurred.
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It is the Bayesian estimate for the same case if certain assumptions are made for the prior distribution of the probability and if a trial yields more information, then the empirical probability can be improved on by adopting further assumptions in the form of the statistical model. If such a model is fitted, then it can be used to derive an estimate of the probability of the specified event.
An advantage of estimating probabilities using empirical probabilities is that this procedure is relatively free of assumptions and for example consider estimating the probability among a population of men that they satisfy two conditions.
The conditions are they are over 6 feet in height and they are less than 6 feet in height as well as they prefer strawberry jam to raspberry jam. A direct estimate is determined by counting the number of men who satisfy both conditions to give the empirical probability of the combined condition and an alternative estimate could be found by multiplying the proportion of men who are over 6feetin height.
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It is combined with the proportion of men who prefer strawberry jam to raspberry jam and this estimate depend only on the assumption that the two conditions are statistically independent.
A disadvantage in using these probabilities arises in estimating probabilities which are either very close to zero or very close to one and in these cases very large sample sizes would be needed in order to estimate such probabilities to a good standard of relative accuracy.
Here the statistical model can help depending on the context. In general, one can hope that such models would provide improvements in accuracy when it is compared to empirical probabilities.
