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Questions tagged [causal-diagrams]

A causal diagram is a directed graph that displays causal relationships between variables in a causal model.

A causal diagram is a directed graph that displays causal relationships between variables in a causal model. A causal diagram includes a set of variables (or nodes). Each node is connected by an arrow to one or more other nodes upon which it has a causal influence. An arrowhead delineates the direction of causality, e.g., an arrow connecting variables A and B with the arrowhead at B indicates that a change in A causes a change in B (with an associated probability). A path is a traversal of the graph between two nodes following causal arrows.

Causal diagrams include causal loop diagrams, directed acyclic graphs, and Ishikawa diagrams.

Causal diagrams are independent of the quantitative probabilities that inform them. Changes to those probabilities (e.g., due to technological improvements) do not require changes to the model.

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Causal Inference A Primer Study Question

I am reading Pearl's Causal Inference book and attempted at solving study question 1.2.4. Here is the entire problem: In an attempt to estimate the effectiveness of a new drug, a randomized experiment is conducted. In all, 50% of the patients are…
disst
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Are there holes in my road map from calculus to malliavin differential geometry, Bayesian hypergraphs, and causal inference?

I've constructed a directed acyclic graph that leads from introductory subjects, such as calculus (single and multivariable) to some of my current interests including causal inference, Bayesian hypergraphs, and Malliavin differential geometry. The…
Galen
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Controlling confounders in a causal diagram. Isn't the backdoor criterion sufficient?

In Judea Pearl's The Book of Why we find the following causal diagram: where $U_1$ and $U_2$ are unobserved variables. The diagram is accompanied by a comment that ensures that neither the back door criterion nor the front door criterion are…
Jsevillamol
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Why are causal inference diagrams so useful or effective?

Is there a short explanation of why Pearl's casual inference diagrams are so highly-regarded, useful or effective? I can't help but think it's just so simple an idea that I can't tell why it could be such a big deal: It's just like a set of…
SBK
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Implications of density with respect to Lebesgue measure in a causal setting

I am familiarizing myself with concepts of causality by working through the book Elements of Causal Inference by Jonas Peters, Dominik Janzing, and Bernhard Schölkopf. They state the following problem (Problem 3.8b): Consider the cyclic structural…
Zelazny
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How to prove d-separation implies conditional independence?

All of the materials I see online just state it as fact. I don't see it as obvious at all. I use this definition of a Belief network. And this is the definition of d-seperation from the textbook:
Sophon Aniketos
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On the Derivation of Judea Pearl's Front-Door Adjustment Formula in The Book of Why

I have a number of related questions about the derivation of the front-door adjustment formula as given on page 236. Here is the derivation. I would have typed it up, but the diagrams at the far right would have been a pain to include. There is a…
Adrian Keister
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Conditional Independence Relations for $X_1\leftarrow X\rightarrow X_2$

Let $X$ be a random variable, and let $X_1:=g_1(X)$ and $X_2:=g_2(X)$. Does it hold that $X\perp \!\!\! \perp X_1 | (X_1, X_2)$? (This statement is made in the proof of Proposition 1 in the appendix of Tschannen et al.…
Ričards Marcinkevičs
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conditioning on the source or target variables in d-separation?

In Pearl's Causality - Models, Reasoning and Inference (2009), he defines d-separation as follows: Let $X\perp\!\!\!\perp Y |Z$ mean "$Z$ d-separates $X$ from $Y$". But there seems to be a weird edge case that satisfies this criterion, but…
user56834
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Causal inference calculus (Bayesian Probability)

Here is my problem: There is a causal Markovian model as follows. By the definition of interventional probability, since $\text{do}(x)$ makes no edges between $X$ and $Z_1, Z_2$, we have $$ P(y\mid \text{do}(x))…
Seunghyeon Yu
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How do I carry out do-calculus on a mediator variable?

I have been trying to get my head around using do-calculus in causal inference, and I've run into a little toy problem that's confused me and my classmates. Imagine you have a DAG for some causal model that is defined by $(X \rightarrow M, M…
Griffin Farrow
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Computing value of noisy-MAX model

I am having trouble computing the remaining probabilities with the use of an interaction model called the noisy-MAX. The noisy-MAX model is an interaction model which helps a network engineer assessing probabilities for the CPT of a Bayesian…
LK4
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Conditional probability distrubution, bivariate normal

I am reading Elements of Causal Inference by Jonas Peters, Dominik Janzing, and Bernhard Schölkopf. In section 3.2 the book defines a structural causal model (SCM) $\mathfrak{C}$: $$C:=N_C$$ $$E:= 4 \times C + N_E$$ where $N_C, N_E…
Zelazny
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Prove d-separation path is blocked as long as NOT conditioning on the collider

Getting into the causality tools. Suppose I have a causal graph $X\to R\to T\leftarrow U.$ I can work out that $R$ and $U$ are independent; i.e., $P(r, u) = P(r)\,P(u).$ Also $X$ and $T$ are conditionally independent given $R;$ i.e., $P(x|t,r) =…
PaulDong
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Why is causal influence between concepts in Fuzzy Cognitive maps represented by membership functions?

We Know that FCM are represented by concepts and Weights or causal influence between the concepts. In order to find the weights, we take the help of an expert that describes the relationship between the two concepts using: 1. negative or positive…
roaibrain
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