- Posterior probability
The

**posterior probability**of arandom event or an uncertain proposition is theconditional probability that is assigned after the relevant evidence is taken into account.The posterior probability distribution of one

random variable given the value of another can be calculated withBayes' theorem by multiplying theprior probability distribution by thelikelihood function , and then dividing by thenormalizing constant , as follows::$f\_\{Xmid\; Y=y\}(x)=\{f\_X(x)\; L\_\{Xmid\; Y=y\}(x)\; over\; \{int\_\{-infty\}^infty\; f\_X(x)\; L\_\{Xmid\; Y=y\}(x),dx$

gives the posterior

probability density function for a random variable "X" given the data "Y" = "y", where* $f\_X(x)$ is the prior density of "X",

* $L\_\{Xmid\; Y=y\}(x)\; =\; f\_\{Ymid\; X=x\}(y)$ is the likelihood function as a function of "x",

* $int\_\{-infty\}^infty\; f\_X(x)\; L\_\{Xmid\; Y=y\}(x),dx$ is the normalizing constant, and

* $f\_\{Xmid\; Y=y\}(x)$ is the posterior density of "X" given the data "Y" = "y".

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**Posterior Probability**— The revised probability of an event occurring after taking into consideration new information. Posterior probability is normally calculated by updating the prior probability by using Bayes theorem. In statistical terms, the posterior probability… … Investment dictionary**posterior probability**— noun The probability of an event given the knowledge of occurrence of other events that bear on it; P( A | B ) as contrasted to P( A ), where A is the sought event and B is the sign or symptom event … Wiktionary**posterior probability**— … Useful english dictionary**Posterior (disambiguation)**— Posterior may refer to:* Posterior (anatomy), the end of an organism opposite to its head ** Buttocks, as a euphemism * Posterior probability, the conditional probability that is assigned when the relevant evidence is taken into account … Wikipedia**Probability**— The likelihood that something will happen. For example, a probability of less than .05 indicates that the probability of something occurring by chance alone is less than 5 in 100, or 5 percent. This level of probability is usually taken as the… … Medical dictionary**Prior probability**— Bayesian statistics Theory Bayesian probability Probability interpretations Bayes theorem Bayes rule · Bayes factor Bayesian inference Bayesian network Prior · Posterior · Likelihood … Wikipedia**Imprecise probability**— The notion of Imprecise probability is used as a generic term to cover all mathematical models which measure chance or uncertainty without sharp numerical probabilities. It includes both qualitative (comparative probability, partial preference… … Wikipedia**Glossary of probability and statistics**— The following is a glossary of terms. It is not intended to be all inclusive. Concerned fields *Probability theory *Algebra of random variables (linear algebra) *Statistics *Measure theory *Estimation theory Glossary *Atomic event : another name… … Wikipedia**Conditional probability**— The actual probability of an event A may in many circumstances differ from its original probability, because new information is available, in particular the information that an other event B has occurred. Intuition prescribes that the still… … Wikipedia**List of probability topics**— This is a list of probability topics, by Wikipedia page. It overlaps with the (alphabetical) list of statistical topics. There are also the list of probabilists and list of statisticians.General aspects*Probability *Randomness, Pseudorandomness,… … Wikipedia