  Astronomical instruments make intensity measurements; any precise
astronomical experiment ought to involve modeling those measurements. People
make catalogues, but because a catalogue requires hard decisions about
calibration and detection, no catalogue can contain all of the information in
the raw pixels relevant to most scientific investigations. Here we advocate
making catalogue-like data outputs that permit investigators to test hypotheses
with almost the power of the original image pixels. The key is to provide users
with approximations to likelihood tests against the raw image pixels. We
advocate three options, in order of increasing difficulty: The first is to
define catalogue entries and associated uncertainties such that the catalogue
contains the parameters of an approximate description of the image-level
likelihood function. The second is to produce a K-catalogue sampling in
"catalogue space" that samples a posterior probability distribution of
catalogues given the data. The third is to expose a web service or equivalent
that can re-compute on demand the full image-level likelihood for any
user-supplied catalogue.
