  When observations are organized into groups where commonalties exist amongst
them, the dependent random measures can be an ideal choice for modeling. One of
the propositions of the dependent random measures is that the atoms of the
posterior distribution are shared amongst groups, and hence groups can borrow
information from each other. When normalized dependent random measures prior
with independent increments are applied, we can derive appropriate exchangeable
probability partition function (EPPF), and subsequently also deduce its
inference algorithm given any mixture model likelihood. We provide all
necessary derivation and solution to this framework. For demonstration, we used
mixture of Gaussians likelihood in combination with a dependent structure
constructed by linear combinations of CRMs. Our experiments show superior
performance when using this framework, where the inferred values including the
mixing weights and the number of clusters both respond appropriately to the
number of completely random measure used.
