Simple Monte Carlo

[drphilmarshall]

@davidthomas5412 Let's start with the simplest possible inference: simple Monte Carlo. We'll need the ForegroundCatalog to be able to set_prior and then draw_halo_masses, and then we'll need to compute_likelihood (using the the function @sweverett already implemented). This will give us N_samples * (N_halos + 1) numbers (if we keep the concentrations fixed for now): this is going to get into the Mb quite quickly, so we might want to think about how to store the samples (we need to keep them all). A quick and easy solution is to write out simple plain text halo catalogs that can be read back in with the existing ForegroundCatalog method, but this won't scale well: let's start thinking about database table design.

[drphilmarshall]

@davidthomas5412 The notebook that addresses this issue should contain a PGM describing what we are doing: let's use that diagram to be clear about what assumptions we are making (eg about the halo concentrations!). If you took a photo of the group meeting whiteboard, feel free to use that (you can make <img href=""> calls from markdown cells. Otherwise, issue me with making the simplest possible inference PGM and I'll provide some daft code.