Although the posterior density given by (1) provides all that is needed for inference about , there may be particular interest in a subset of of dimension2 . where
and, if is of dimension ,
Denoting the complement of with respect to as , then the Bayesian paradigm gives inference for as the marginal posterior density
where is the parameter space supporting , i.e. the appropriate region of integration for the subset of .
In a similar way, inference about , when are known, is given by the conditional posterior density