10/4 hierarchical sbi conversation (Sree, Becky, Jason)

[beckynevin]

• Reviewed Jason’s paper section about hierarchical SBI; main point is that hierarchy is sharing information between levels in a structured way
• Reviewed the hierarchy slide deck and the definition of hierarchy, levels (groups), and multilevel, talked about 8 schools example and why it’s hierarchical
• Going over strong lensing PGM (probabilistic graphical model). Cosmology is grouped by universe, einstein radius is estimated for each image individually, drawing from cosmology according to universe group
• Talked about how to make SBI hierarchical (w/i the simulator)
  https://github.com/deepskies/DeepUQ/blob/issue/SBI_shape_and_hierarchy/notebooks/SBI.ipynb

Decided we need a separate .csv file from a code that saves (x,θ) pairs where θ is all parameters from all levels (including ag)
sbi will then use this as the training set ^
Also discussed priors, where priors on intermediate parameters like ag need to have conditional priors p(ag|mu_a_g, sigma_a_g) where mu_a_g and sigma_a_g are specific values
^Does it make sense to make a prior for ag that is essentially different at all different values of mu_a_g and sigma_a_g? This would potentially need to have a lookup fxn
This is looking a lot like a wrapper for sbi, maybe it’s best to reach out to mackelab via the issues

Action items:

• Becky - Put these notes into discussion format on github
• Becky & Sree - work together to make a mackelab issue asking about this idea
• Becky - incorporate probabilities into the pendulum PGM
• Sree - lensing PGM
• Becky - write (x,θ) pairs to disk
• Becky & Sree - cowork on code
• Becky, Sree, Jason - meet again about how to input the above “weird” prior