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@djinnome djinnome commented Jul 29, 2025

Summary of changes:

  • References to Causal Hierarchical models PR Hierarchical Causal Models #236 have been moved to Future work section
  • y0 replaced by $Y_0$ on line 136
  • In the Summary, we specify that not only does the output of the identification algorithm give a qualitative answer as to whether a query is identifiable, but also that it provides guidance on how to transform the causal query into a symbolic estimand that can be non-parametrically estimated from the available data.
  • On line 99, ($\pi_1$) now specifies that the interventional data comes from a study that randomized on smoking, but only measured its effect on tar accumulation in the lungs (a surrogate outcome), not the effect of smoking on cancer. By combining observational data associating smoking with tar and cancer ($\pi^\ast$) with interventional data on the surrogate outcome ($\pi_1$), we show we can identify the causal effect of smoking on cancer.
  • Instead of using PN, PS, and PNS, we provide a complete specification of associational, interventional and counterfactual symbolic probabilistic expressions, and their representation in the DSL.
  • We demonstrate that the associational expression: $P(Y=y | X=x^\ast)$, is represented as: P(Y | ~X)
  • Likewise, the interventional expression $P_{do(X=x~\ast)}(Y, Z)$ is represented as P[~X](Y,Z).
  • Finally, the counterfactual expression $P(Y_{do(X=x^\ast)}=y^\ast\mid X=x, Y=y)$ is represented as P(~Y @ ~X | X, Y).
  • Cleaned up future work so that it cited actual algorithms to implement, rather than speculating about the possibility of future algorithms to implement.
  • added newly cited algorithms to bibliography.

@djinnome djinnome linked an issue Jul 29, 2025 that may be closed by this pull request
@djinnome djinnome requested a review from cthoyt July 29, 2025 04:37
@cthoyt cthoyt merged commit cefdedf into main Jul 29, 2025
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@cthoyt cthoyt deleted the 308-resolve-inconsistencies-in-presentation branch July 29, 2025 09:19
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cthoyt commented Jul 29, 2025

thanks @djinnome! I did some light editing and merged this

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Resolve inconsistencies in presentation

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