Posterior probability

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Posterior Probability

Posterior probability (pronunciation: poh-stee-er-i-or prob-uh-bil-i-tee) is a term used in Bayesian statistics to describe the revised probability of an event occurring after taking into consideration new information.

Etymology

The term "posterior" in this context is derived from Latin, meaning "after" or "following". The term "probability" comes from the Latin "probabilitas", which can mean "provable", "probable", or "likely". Together, they form the concept of "posterior probability", which is the likelihood of an event following the acquisition of additional data.

Definition

In Bayesian statistics, the posterior probability is the updated probability of a hypothesis given evidence. It is calculated using Bayes' theorem, which is a fundamental theorem in probability theory and statistics that describes how to update the probabilities of hypotheses when given evidence.

Related Terms

  • Prior probability: The probability of an event before new data is collected.
  • Likelihood function: A function of the parameters of a statistical model given specific observed data.
  • Bayes' theorem: A theorem describing how to update the probabilities of hypotheses when given evidence.
  • Bayesian inference: A method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available.

Calculation

The posterior probability is calculated using Bayes' theorem. The formula is as follows:

P(H|E) = [P(E|H) * P(H)] / P(E)

Where:

  • P(H|E) is the posterior probability
  • P(E|H) is the likelihood
  • P(H) is the prior probability
  • P(E) is the evidence

Applications

Posterior probability has wide applications in fields such as medicine, machine learning, artificial intelligence, and data science. It is used to update the probability of a hypothesis based on new evidence.

External links

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