Posterior probability

The Posterior probability, in Bayesian statistics, is the revised probability of an event occurring after taking into consideration new information. It contrasts with the prior probability, which is the probability of an event before new data is collected. The posterior probability is calculated using Bayes' theorem.

Definition

The posterior probability is defined as the probability of event A given event B, written as P(A|B). It is calculated using the formula:

P(A|B) = [P(B|A) * P(A)] / P(B)

Where:

• P(A|B) is the posterior probability
• P(B|A) is the likelihood
• P(A) is the prior probability
• P(B) is the marginal likelihood

Application

Posterior probability is widely used in various fields such as medicine, engineering, and finance. In medicine, for example, it can be used to determine the probability of a disease given the result of a medical test.

See also

• Bayesian inference
• Conditional probability
• Prior probability
• Likelihood function
• Marginal likelihood