observed quantities with high accuracy.

With the accumulation of data from large galaxy surveys over the last decade, a third method has been developed, which links galaxies to halos using a statistical approach. The Halo Occupation Distribution (HOD) formalism specifies the probability distribution for a halo of mass $M$ to harbour $N$ galaxies with certain intrinsic properties, such as luminosity, color, or type [e.g. @peacock2000; @seljak2000; @white2001; @berlind2002]. More complex formulations of this kind of modelling, such as the conditional luminosity function (CLF) formalism [@yang03; @vdb2003; @yang04] have extended the HOD approach. These methods have the advantage that they do not rely on assumptions about the (poorly understood) physical processes that drive galaxy formation. In this way, it is possible to constrain the relationship between galaxy and halo properties (and thus, indirectly, the underlying physics), and to construct mock catalogs that reproduce in detail a desired observational quantity (such as the luminosity function). One disadvantage of the classical HOD approach was that one had to make assumptions about the distribution of positions and velocities of galaxies within their host halos. In addition, the results of the HOD modelling can be difficult to interpret in terms of the underlying physics of 