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Bayesian statistics |
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Posterior = Likelihood × Prior ÷ Evidence |
Background |
Model building |
Posterior approximation |
Estimators |
Evidence approximation |
Model evaluation |
The posterior probability is a type of conditional probability that results from updating the prior probability with information summarized by the likelihood via an application of Bayes' rule.[1] From an epistemological perspective, the posterior probability contains everything there is to know about an uncertain proposition (such as a scientific hypothesis, or parameter values), given prior knowledge and a mathematical model describing the observations available at a particular time.[2] After the arrival of new - posterior or later in time - information, the current posterior probability may serve as the prior in another round of Bayesian updating.[3]
In the context of Bayesian statistics, the posterior probability distribution usually describes the epistemic uncertainty about statistical parameters conditional on a collection of observed data. From a given posterior distribution, various point and interval estimates can be derived, such as the maximum a posteriori (MAP) or the highest posterior density interval (HPDI).[4] But while conceptually simple, the posterior distribution is generally not tractable and therefore needs to be either analytically or numerically approximated.[5]
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