Talk:Causal model

Definition(s)
In response to this remark I have found several definitions looking for "a causal model is" in Google-books, for example: Now I am not sure how this could be integrated into the article, but could be a good start. -- Mdd (talk) 21:13, 9 April 2011 (UTC)
 * "According to a formal definition, a causal model is a mathematical object that provides an interpretation and computation of causal queries about the domain [Galles & Pearl 1998]..."
 * "A causal model is composed by a set of logical formulae which expresses different kinds of relationships among entities belonging to different types..."
 * "A causal model is an advanced form of dependency model that allows modelling the various scenarios that can lead to a defined state - in our case, the winding down of a ..."
 * "A causal model is a unique model describing the mechanisms of the system..."

Expansion
Just did a vast expansion of this. Feedback encouraged. Particular items: TIA. Lfstevens (talk) 14:17, 28 October 2018 (UTC)
 * Errors. This is a complex subject. Please flag any errors and I will fix them.
 * Organization. The major source of the piece is Pearl's book. It only sort of uses the organization I ended up adopting. I'd appreciate your suggestions for how to improve that bit (and anything else, for sure).
 * Clarity. This piece is pretty abstract. The book does a better job than the article of including examples as a path to clarity. For brevity, I left most of this out and shifted the focus to more abstract concerns. Are more examples needed? Where? Are Pearl's examples the ones to go with?

Is causal model falsifiable?
The article claims causal model is falsifiable: "Causal models are falsifiable, in that if they do not match data, they must be rejected as invalid."

However, this appears very different from the definition of falsifiable: "A theory or hypothesis is falsifiable (or refutable) if it can be logically contradicted by an empirical test that can potentially be executed with existing technologies." on https://en.wikipedia.org/wiki/Falsifiable.

The latter definition makes more sense to me. If that definition is more wide accepted, should the falsifiability claim in this article be removed or corrected? — Preceding unsigned comment added by 50.234.189.45 (talk) 21:39, 7 December 2022 (UTC)

Add: this claim was added on 23:17, 27 October 2018‎. Before that, there was a specific claim on A->B->C model can be falsified. However, that claim was not based on the latter definition of falsifiability. Even if that claim holds, it remains a question whether it not generalize to all causal models. — Preceding unsigned comment added by 50.234.189.45 (talk)

Interventional Distribution is missing
https://www.pymc.io/projects/examples/en/latest/causal_inference/interventional_distribution.html See where the example is given that the joint distribution defined by a specific DAG is $$P(x_1, x_2, x_3, x_4, x_5) := P(x_1) P(x_3|x_1) P(x_2|x_1) P(x_4|x_3, x_2) P(x_5|x_4)$$ while the interventional distribution for $$x_3=1$$ removes all terms which would influence $$X_3$$: $$P(x_1, x_2, \operatorname{do}(x_3=1), x_4, x_5) = P(x_1) P(x_2|x_1) P(x_4|x_3=1, x_2) P(x_5|x_4)$$. This seems to imply that the distribution $$P(x_1, x_2, \operatorname{do}(x_3=1), x_4, x_5)$$ can be estimated from the observed data by completely filtering out all cases where $$x_3 \neq 1$$ and looking at the remaining observations which especially implies differnt normalization ...?? I cite from https://www.inference.vc/untitled/ "the conditional distribution takes the population of data points (x', y') ~ p(X, Y) and filters to the subpopulation where X = x; 2. the interventional distribution sets X = x in the generative process and simulates forward". I also guess that the toy example from https://www.inference.vc/causal-inference-2-illustrating-interventions-in-a-toy-example/ would be valuable to be added! Biggerj1 (talk) 23:14, 17 May 2024 (UTC)