What Is an Empirical Probability?

The empirical probability refers to the probability of an event's success or failure estimated from experience. For example, in n trials, event A occurs m times, and the ratio m / n is the relative frequency of event A success. If, as the total number of tests increases, the ratio m / n of the number of successful times m to the number of tests n tends to a constant, this constant is the empirical probability. ^[1]

Empirical probability

The following is from some wikis

Empirical probability or experimental probability, also known as relative frequency, refers to the ratio of the number of times a specific event occurs to the total experimental sample ^[3]

One of the great advantages of using empirical probability to estimate probability is that this method requires relatively few assumptions.

For example, estimate the probability of a group of men who meet two conditions:

a. They are over six feet tall;

b. They prefer strawberry jam over raspberry jam.

The direct estimation method is to count the number of men who meet these two conditions at the same time to obtain the empirical probability value. Another estimation method can first calculate the proportion of men who are over six feet tall and the ratio of those who prefer strawberry jam over raspberry jam.

Using empirical probability estimates to estimate probabilities can be problematic when the probability is very low or very high (close to 0 or 1). In this case, we need a very large sample size to ensure the relative accuracy of the estimate. At this time, we can use statistical models to make estimates based on specific situations. Generally speaking, such models can help improve the accuracy of empirical probabilities if the assumptions hold.

For example, to estimate the probability that the lowest daily maximum temperature in February of any year is below zero. Temperatures from the past few years can be used to estimate this probability. Or you can choose a probability distribution model and use it to fit observations from the past few years. A well-fitted distribution model can be used to estimate the probability we need. Using this method, we can still make a probability estimate even if the highest temperature on this day has been above zero for all odds.

3. Confused concepts:

In English, empirical probability is sometimes called inductive probability, and it is important not to be confused with posterior probability in Bayesian theory. An i is added after the first word of the former.