Advantages An advantage of estimating probabilities using empirical probabilities is that this procedure is relatively free of assumptions. For example, consider estimating the probability among a population of men that they satisfy two conditions: • that they are over 6
feet in height. • that they prefer strawberry jam to raspberry jam. A direct estimate could be found by counting the number of men who satisfy both conditions to give the empirical probability of the combined condition. An alternative estimate could be found by multiplying the proportion of men who are over 6 feet in height with the proportion of men who prefer strawberry jam to raspberry jam, but this estimate relies on the assumption that the two conditions are
statistically independent.
Disadvantages A disadvantage in using empirical probabilities arises in estimating probabilities which are either very close to zero, or very close to one. In these cases very large sample sizes would be needed in order to estimate such probabilities to a good standard of relative accuracy. Here
statistical models can help, depending on the context, and in general one can hope that such models would provide improvements in accuracy compared to empirical probabilities, provided that the assumptions involved actually do hold. For example, consider estimating the probability that the lowest of the daily-maximum temperatures at a site in February in any one year is less than zero degrees Celsius. A record of such temperatures in past years could be used to estimate this probability. A model-based alternative would be to select a family of
probability distributions and fit it to the dataset containing past years′ values. The fitted distribution would provide an alternative estimate of the desired probability. This alternative method can provide an estimate of the probability even if all values in the record are greater than zero. ==Mixed nomenclature== The phrase
a-posteriori probability is also used as an alternative to "empirical probability" or "relative frequency". ==See also==