# Conditional Probability Value

(Redirected from posterior probability)

A conditional probability value is a probability value of an event, *A*, and of one or more guaranteed events.

**AKA:**Aposteriori Probability, Posterior Probability.**Context:**- It can be the output of a Conditional Probability Function.
- It can be a member of a Conditional Probability Distribution, such as in a Joint Probability Table.

**Example(s):**^{1}/_{2}is the conditional probability that a Two-Dice Experiment will result in two even numbers if you know that one of the dice is guaranteed to be even.

**Counter-Example(s):****See:**Apriori Probability Value/Prior Probability Value; Posterior Probability Distribution; Bayesian Methods.

## References

### 2015

- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/posterior_probability Retrieved:2015-6-15.
- 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. Similarly, the posterior probability distribution is the probability distribution of an unknown quantity, treated as a random variable, conditional on the evidence obtained from an experiment or survey. "Posterior", in this context, means after taking into account the relevant evidence related to the particular case being examined.

- In Bayesian statistics, the

### 2011

- (Webb, 2011j) ⇒ Geoffrey I. Webb. (2011). “Posterior Probability.” In: (Sammut & Webb, 2011) p.780
- QUOTE: In Bayesian inference, a posterior probability of a value x of a random variable X given a context a value y of a random variable Y, P(X = x | Y = y), is the probability of X assuming the value x in the context of Y = y. It contrasts with the prior probability, P(X = x), the probability of X assuming the value x in the absence of additional information.
For example, it may be that the prevalence of a particular form of cancer, exoma, in the population is 0.1%, so the prior probability of exoma, P(exoma = true), is 0.001. However, assume 50% of people who have skin discolorations of greater than 1 cm width (sd > 1cm) have exoma. It follows that the posterior probability of exoma given sd > 1cm, P(exoma = true | sd > 1cm = true), is 0.500.

- QUOTE: In Bayesian inference, a posterior probability of a value x of a random variable X given a context a value y of a random variable Y, P(X = x | Y = y), is the probability of X assuming the value x in the context of Y = y. It contrasts with the prior probability, P(X = x), the probability of X assuming the value x in the absence of additional information.

### 2007

- (WordNet, 2007) ⇒ http://wordnet.princeton.edu/perl/webwn?s=conditional%20probability
- QUOTE: the probability that an event will occur given that one or more other events have occurred

### 2000

- (Valpola, 2000) ⇒ Harri Valpola. (2000). “Bayesian Ensemble Learning for Nonlinear Factor Analysis." PhD Dissertation, Helsinki University of Technology.
- QUOTE: posterior probability: Expresses the beliefs after making an observation. Sometimes referred to as the posterior.