Bayesian inference is the process of using a Bayesian model to draw conclusions about an unknown parameter
or unobserved data. Given observed data 
, a likelihood function 
, and a prior
distribution with density 
, Bayes' theorem gives
the posterior distribution with density
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For a discrete parameter, the integral in the denominator is replaced by a sum.
The resulting posterior distribution may be summarized to estimate the parameter, predict unobserved data, compare models, or choose actions using a loss function. The uncertainty in these conclusions is therefore conditional on both the observed data and the assumptions encoded in the Bayesian model.
