non-separable and generative random catalogs

Standard practice in large-scale structure is to make large-scale structure and cross-correlation measurements using a catalog of tracers (quasars in our case now) with random catalogs taking the role of tracking the selection function. In most cases this random catalog is made by sampling from a model for the angular selection function and, separately, for each object, sampling from a model for the radial selection function (redshift distribution in our case now). But of course the redshift distribution depends, in detail, on the angular selection function (because, for example, some of the angular selection is set by dust extinction). Kate Storey-Fisher (NYU) and I discussed now to capture these issues in the random we are building for the ESA Gaia quasar sample we are using. One idea is to give the randoms quasar-like luminosities and building the random catalog using our causal ideas about how things make it into the catalog