Posterior probability is the conditional probability assigned to an event or hypothesis
after specified data have been taken into account. For a hypothesis 
and data 
with 
, Bayes' theorem gives
 |
where 
is the prior probability and 
is the likelihood of the
data under 
.
If 
are mutually exclusive and exhaustive hypotheses,
then
 |
When an unknown parameter is discrete, its posterior probabilities form a posterior distribution. For a continuous parameter, an individual value typically has probability zero, so uncertainty is described using a posterior probability density function or probabilities of intervals.
