Editing Information content (section)

{{short description|Basic quantity derived from the probability of a particular event occurring from a random variable}}
{{cleanup|reason=unclear terminology|date=June 2017}}

In [[information theory]], the '''information content''', '''self-information''', '''surprisal''', or '''Shannon information''' is a basic quantity derived from the [[probability]] of a particular [[Event (probability theory)|event]] occurring from a [[random variable]]. It can be thought of as an alternative way of expressing probability, much like [[odds]] or [[log-odds]], but which has particular mathematical advantages in the setting of information theory.

The Shannon information can be interpreted as quantifying the level of "surprise" of a particular outcome. As it is such a basic quantity, it also appears in several other settings, such as the length of a message needed to transmit the event given an optimal [[Shannon's source coding theorem|source coding]] of the random variable.

The Shannon information is closely related to ''[[Entropy (information theory)|entropy]]'', which is the expected value of the self-information of a random variable, quantifying how surprising the random variable is "on average". This is the average amount of self-information an observer would expect to gain about a random variable when measuring it.<ref>Jones, D.S., ''Elementary Information Theory'', Vol., Clarendon Press, Oxford pp 11–15 1979</ref>

The information content can be expressed in various [[units of information]], of which the most common is the "bit" (more formally called the ''shannon''), as explained below.

The term 'perplexity' has been used in language modelling to quantify the uncertainty inherent in a set of prospective events.{{Citation needed|reason=This is not common knowledge, needs a source|date=May 2025}}