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> Methods like propensity matching, propensity weighting, and hierarchical models using different treatment levels as strata, are absolutely critical for applying this stuff in the real world.

Have you got some readings? I've been reading the Pearl books on this subject.

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A good starting point is chapters 9 & 10 from [0]. Then many of the same topics are re-discussed in the second half of the book through the lens of Bayesian hierarchical models.

Another good reference is [1]. Rubin invented a lot of observational data methods for correcting to measure causal effect. Imbens is also a prolific author in this area, and even just googling for propensity model papers from Imbens will leads to many methods and many other papers.

[0]: < http://www.stat.columbia.edu/~gelman/arm/ >

[1]: < https://www.amazon.com/Causal-Inference-Statistics-Biomedica... >

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