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 dimension^{2} . 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*

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