Infer shared parameters roadmap

A roadmap for starting to infer "shared" parameters in contrast to per-source parameters. Examples are:

1. The number of sources in a part of the sky (governed by a Poisson process with smoothly varying rate)
2. The background image
3. The sky noise (epsilon)
4. The optical sensitivity (iota)
5. The point spread function

• Optionally (pending accuracy gains) using something other than convolutions of mixtures of normals:
  • A sparse dictionary of pixels
  • An autoencoder
• Varying smoothly over the image somehow:
  • A polynomial in the parameters
  • A Gaussian process

At a high level, here are the steps required to make progress in the short term:

1. Render a sparse image without the PSF convolution.

• To allow a pixellated PSF, we must over-sample the actual sky image.
• Use a sparse matrix to represent the rendered sky
• Use a FFT with a pixellated PSF and compare the algorithm time

1. Switch to a Gaussian model from a Poisson model

• The approximation to the Poisson log term means the star and galaxy inferences are not separable
• When inferring sources rather than using a catalog init, it will be helpful to fit star models separately from galaxy fits for faster inference.
• The observations are nearly Normal anyway
• Requires passing in / inferring the per-pixel noise (poisson noise + "dark variance")
• The existing optimization will probably be more robust
• Modelling spatially correlated noise will be much easier

1. Infer the number of objects in an image / avoid catalog init

• Will require a possible "this is not an object" value for the object type indicator
• Add a Poisson process for object counts that varies smoothly across the sky