What is the difference between prior and posterior probabilities

The difference between prior and posterior probabilities characterizes the information we have gotten from the experiment or measurement. In this example the probability changed from 0. Note also the surprising result in this case, which, although hypothetical, is typical of many medical screening tests. This is due to the very low proportion of actually-infected people in the population -- most of the positive test results are false positives from the non-infected people who are being tested.

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List of Partners vendors. A posterior probability, in Bayesian statistics, is the revised or updated probability of an event occurring after taking into consideration new information.

The posterior probability is calculated by updating the prior probability using Bayes' theorem. In statistical terms, the posterior probability is the probability of event A occurring given that event B has occurred. The formula to calculate a posterior probability of A occurring given that B occurred:. The posterior probability is thus the resulting distribution, P A B.

Bayes' theorem can be used in many applications, such as medicine, finance, and economics. In finance, Bayes' theorem can be used to update a previous belief once new information is obtained. Prior probability represents what is originally believed before new evidence is introduced, and posterior probability takes this new information into account. Posterior probability distributions should be a better reflection of the underlying truth of a data generating process than the prior probability since the posterior included more information.

A posterior probability can subsequently become a prior for a new updated posterior probability as new information arises and is incorporated into the analysis. If f i x is the normal distribution, then:. The term in square brackets is called the generalized squared distance of x to group i and is denoted by d i 2 x. The term in square brackets is the linear discriminant function.

The only difference from the case without prior probabilities is a change in the constant term. Notice, the largest posterior is equivalent to the smallest generalized distance, which is equivalent to the largest linear discriminant function.

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