Propensity score latent - DRAFT

[NathanielF]

Working on a draft PR to improve or augment the existing propensity scoring weighting implementation. In particular to make it a bit faster and more "Bayesian". As it currently stands we are performing a two-step strategy where we fit a propensity score model and then push the values of the posterior estimate for the propensity score through a re-weighting routine to estimate the causal contrast.

But we could try and explore a more properly Bayesian model where we fit the propensity score outcome and the model outcome at once in the same model context. This more properly Bayesian and a good bit faster.

See for instance, work here: https://github.com/ajnafa/Latent-Bayesian-MSM by Jordan Nafa and Andrew Heiss

Adding a POC notebook to start

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📚 Documentation preview 📚: https://causalpy--500.org.readthedocs.build/en/500/

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Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 94.59%. Comparing base (fdce5b0) to head (96098cb).

Additional details and impacted files

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  Coverage   94.59%   94.59%           
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  Files          28       28           
  Lines        2053     2053           
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  Hits         1942     1942           
  Misses        111      111           

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