All the complex models featured in ·~his volume may be viewed as the specification of a joint distribution of observables (data) and unobservables (model parameters, missing data or latent variables). Often the model can be represented as a directed acyclic graph (Lauritzen and Spiegelhalter, 1988; Whittaker, 1990) in which case this joint density can be immediately written down (see Gilks, 1995: this volume). In some cases, such as in spatial modelling, this joint density is uniquely determined through suitable local specification (Besag and Green, 1993). Regardless, it is this joint density whose performance must be examined with respect to model determination.