Posterior probability
Conditional probability used in Bayesian statistics / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Posterior probability?
Summarize this article for a 10 year old
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 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]