Bayesian statistics

Bayesian Statistics

Bayesian statistics (pronunciation: /ˈbeɪziən/), is a theory in the field of statistics based on the Bayesian interpretation of probability where probability expresses a degree of belief in an event. The degree of belief may be based on prior knowledge about the event, such as the results of previous experiments, or on personal beliefs about the event.

Etymology

The term "Bayesian" refers to Thomas Bayes (/ˈbeɪz/), who proved a special case of what is now called Bayes' theorem in a paper presented in 1763.

Related Terms

Bayes' theorem: In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule) describes the probability of an event, based on prior knowledge of conditions that might be related to the event.

Prior probability: In Bayesian statistical inference, a prior probability distribution, often simply called the prior, of an uncertain quantity is the probability distribution that would express one's beliefs about this quantity before some evidence is taken into account.

Posterior probability: In Bayesian statistics, the posterior probability of a random event or an uncertain proposition is the conditional probability that is assigned after the relevant evidence or background is taken into account.

Likelihood function: In statistics, a likelihood function (often simply the likelihood) is a function of the parameters of a statistical model, given specific observed data.

Statistical model: A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data (and similar data from a larger population).

Probability distribution: In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment.

Conditional probability: In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event has already occurred.