## Marginal and conditional densities

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

 (6)

and, if is of dimension ,

 (7)

Denoting the complement of with respect to as , then the Bayesian paradigm gives inference for as the marginal posterior density

 (8)

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

 (9)

danny 2009-07-23