mixture of delta functions, roulette

On the weekend, Adam Bolton (Hawaii) and I had a long discussion of modeling images, possibly as mixtures of delta functions (which, when convolved with the PSF, are a reasonable and complete basis for modeling any image). My interest is understanding multiwavelength data at the angular resolution of the highest resolution image (or better). This involves not just modeling the pixels, but also modeling spectral-energy-distribution space. We discussed using a delta-function sampling of this too.

Today, Bovy and I continued this discussion, with thoughts about how to generalize the pixel-space and SED-space models to other kinds of mixtures or linear subspaces. This is a non-trivial issue, because choices made here probably affect issues related to optimization, error analysis, and sampling, all of which will come much later.

A long email conversation among Bovy, Lang, Scott Tremaine (IAS) and I continued over our Bayesian formulation of the orbital roulette problem. This is all getting very philosophcal, but Bovy and I are taking the position that the statement of roulette is the statement that the posterior probability distribution of phase, for each object taken individually, is flat. This becomes a constraint on the permitted priors. Tremaine had hoped that roulette could be derived from Bayesian considerations, not that it would be an assumption modifying the Bayesian inputs.