Gibbs Sampled Toy Model

[drphilmarshall]

Seems like some of our sampling problems (eg inconsistent treatment of H0, additional "false" scatter in sigma parameters due to sampling noise) might go away if we switch to Gibbs sampling all parameters and hyper-parameters simultaneously. However, this is not going to be without its pitfalls either. We decided to investigate the behaviour of Gibbs sampling in the simplest possible problem. Here's what we need to do:

• [x] Define toy problem and draw its PGM: #11, done.
• [ ] Code up the generation of mock data
• [ ] Code up a Gibbs sampler
• [ ] Test our inference of the hyper -parameters for a range of 1) numbers of objects in the ensemble and 2) the scale (obs error / intrinsic scatter)

Documentation of code and results in a notebook is tracked at #11.

[drphilmarshall]

Notebook is now up, here. If the mock data and Gibbs sampler are done, you can check off those items, @astrosonnen. Perhaps we need an additional checkbox for the analytic comparison? You can edit the first comment in this thread.