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:

• "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]..." [1]
• "A causal model is composed by a set of logical formulae which expresses different kinds of relationships among entities belonging to different types..." [2]
• "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 ..." [3]
• "A causal model is a unique model describing the mechanisms of the system..." [4]

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)

Expansion

Just did a vast expansion of this. Feedback encouraged. Particular items:

• 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?

TIA. Lfstevens (talk) 14:17, 28 October 2018 (UTC)

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)