Support for Posterior SBC and misc

[Cab14bacc]

Closes #12 and referenced #49
Depends on #53 and #52

This PR introduces support for Posterior SBC using PyMC Models. Given original posterior samples, generate posterior predictive samples, augment them with the original observed data, sample from posterior conditioned on the augmented data, and compute rank statistics comparing the original posterior samples and the augmented posterior samples.

Constraint of Implmentation

Posterior SBC augments the observed data (concatenating original + replicated), which changes its size. For this to work, store observed data in pm.Data containers, and specify size using the dims parameter instead of setting a static shape.

If your model uses dims and coords, you are also responsible for resizing them to the correct size corresponding to the new augmented dataset via the update_data callback. Similarly, if your model has covariates, store them in pm.Data so they can be resized in the same callback.

New Parameters for SBC Class

• method="posterior": You can now pass an original trace (containing posterior distributions) alongside method="posterior" to execute Posterior SBC.
• Custom Callbacks: These are included to deal with needed updates to the model when conditioning on the augmented dataset.
  • augment_observed: Custom logic for how to augment the posterior predictive sample and the observed data, the default behavior is to concatenate on the first axis.
  • update_data: Called before conditioning on the augmented dataset. custom logic to update the covariates, coords to conform to the new augmented data. There is no default behavior, but if user does not modify variable that are of type pm.Data that are used for observed data, the code will update according to the augmented data.

Misc

• Added tests for posterior sbc.
• Added toy example for posterior sbc.

[aloctavodia]

Better to restrict this PR to posterior SBC and have separate PRs for other features like bug fixes, new functions, etc.