Editing Information content (section)

=== Relationship to log-odds ===
The Shannon information is closely related to the [[log-odds]]. In particular, given some event <math>x</math>, suppose that <math>p(x)</math> is the probability of <math>x</math> occurring, and that <math>p(\lnot x) = 1-p(x)</math> is the probability of <math>x</math> not occurring. Then we have the following definition of the log-odds:
<math display="block">\text{log-odds}(x) = \log\left(\frac{p(x)}{p(\lnot x)}\right)</math>

This can be expressed as a difference of two Shannon informations:
<math display="block">\text{log-odds}(x) = \mathrm{I}(\lnot x) - \mathrm{I}(x)</math>

In other words, the log-odds can be interpreted as the level of surprise when the event ''doesn't'' happen, minus the level of surprise when the event ''does'' happen.