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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.

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Mediators in Causal Diagrams

I've been reading Judea Pearl's The Book of Why to try to understand how to use causal diagrams. On page 113, Pearl gives three events, A, B, and C, where A causes B which causes C. This is displayed ...
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Causal Graph Generation from Joint Probability Distribution and Conditional Probability

I am trying to find a causal graph from this data. ...
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Clarification on the properties of double summation in causal inference

Below is the proof along with the causal graph I copied from a textbook about causal inference by Brady Neal: Claim Given the causal graph is Figure A.1, $P(m \mid d o(t))=P(m \mid t)$. START OF THE ...
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In a Bayesian network, does the removal of an edge ever remove existing conditional independences?

I am wondering if the removal of any edge in a acyclic Bayesian network ever removes an existing conditional independence? Intuitively, I would think not, but I was wondering if there is a formal ...
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Exact solution to Dirac delta perturbation for particle in a box

Using diagrammatic perturbation theory the energy of a particle in a box with a Dirac delta potential can be closely approximated. The following energy correction terms to the ground state energy ($\...
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Block Diagram - $x(t)$ and $y(t)$, but $y(t)$ does not exist, only $y'(t)$

I have the transfer function: $$H\left(s\right)=\frac{s+50}{s\left(s+1\right)\left(s+3\right)}=\frac{Y\left(s\right)}{X\left(s\right)}$$ and: $$H_1\left(s\right)=\frac{1}{s\left(s+1\right)\left(s+3\...
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Interventional query without adjustment set

Given the following casual graph, we need to find the formula for $P(y|do(a))$ in terms of observed variables Y, A, W, M. My attempt is to try different back-door and front-door adjustment sets, ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 \...
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Splitting of square diagram in chain complexes

Let us consider a square in chain complexes over a field $k$ \begin{array}{ccc}A & \xrightarrow{f} & B \\ \downarrow{g} & & \downarrow{h} \\ C & \xrightarrow{k} & D\end{array} ...
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Let X, Y, Z and W be sets defined on the universal set $U = N $ as follows: How can I solve this Venn Diagram?

So I have the following assertions and I have to illustrate this on a Venn Diagram. $ (X - Y) \cap Z = ${1,2,3,4} $ Y = $ {5,6} $Z \cap Y = \emptyset $ $ W \cap (X - Z) =$ {7,8} $ X \cap W \cap ...
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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:
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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 ...
Adrian Keister's user avatar
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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 ...
Ričards Marcinkevičs's user avatar
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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 ...
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For a structured causal model, if two RVs are conditionally independent on X, are they also independent when only one of them is conditioned on X?

Does $(A \perp B)|X$ implies $(A|X)\perp B$ ? I managed to derive it, but it feels wrong. Here is my derivation. Is it flawed? If $(A \perp B)|X$ then $(A|X) \perp (B|X)$ and therefore $p[A|(X, (...
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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 ...
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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 ...
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Responses to the study questions from Causal Inference in Statistics (by Judea Pearl).

Does anybody know a source where the correct answers to study questions from the mentioned book are described? I would like to validate whether my way of thinking is correct. I have found only two ...
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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 ...
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Combining P-Values from multiple trials of the same experiment

this is my first question here, a little background about me, im a biomedical engineer, im studying a PhD in Neuroscience, and a Micromaster in Statistics and Data Science. Here in my lab, very few ...
Miguel Núñez Ochoa's user avatar
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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 ...
Jsevillamol's user avatar
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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 ...
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If we have two non-zero-correlated random variables, then why do we say that "correlation does not imply causation"?

If we have two non-zero correlated random variables then they are dependent. Why then do we have the saying "Correlation does not imply Causation". A change in one variable may not cause exactly the ...
usainlightning's user avatar