Mathematics

Questions tagged [causality]

Use for any questions relating to understanding if one entity causes another. This can be at any of the three rungs of causality: association, intervention, or counterfactual. Topics included are do-calculus, causal diagrams, analysis of confounding, $d$-separation, back-door criterion, back-door adjustments, front-door adjustments, instrumental variables, and mediation analysis, among others.

66 questions
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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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Rigorous book on causal inference

Causal Inference is sort of a branch of statistics that defines a new operator called do . I was wondering if there are suggestions of rigorous mathematical books on the subject. Most of what I’ve seen, for example, does not even mentions measure…
Davi Barreira
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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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Conditional covariance of two independent normal variables when their sum is fixed

I am reading through Brady Neal's "Introduction to Causality" course textbook and have got to Section 3.6 where Berkson's paradox is discussed. Neal provides the following toy example: $$ X_{1} = \mathcal{N}(0,1) \\ X_{3} = \mathcal{N}(0,1) \\ X_{2}…
Nick Bishop
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How do I make counterfactual forecasts with do-calculus (Bayesian causality)?

I've been doing a lot of research into Pearl's do-calculus, particularly this paper http://ftp.cs.ucla.edu/pub/stat_ser/r350.pdf . I definitely understand the difference between P(y | x0) and P(y | do(x0)), and why it is important (both…
Sinnombre
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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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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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Can two foliations of Minkowski spacetime share the same spacelike hypersurface?

I have a series of naive questions regarding the question in the title. Let $\mathcal{S}_1$ be a family of spacelike hypersurfaces $\{\Sigma_1\}$ in $\mathbb{M}$ . Let $\Sigma$ be one of these spacelike hypersurfaces. Can I always find (infinitely…
Samuel Fedida
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Formal definition of potential outcomes in causal inference

I find the common potential outcomes notation used in causal inference somewhat confusing. Given a binary exposure $X$ and an outcome $Y$ , the expression $Y_i(1)$ (sometimes also denoted $Y_{1,i}$ or $Y^1_i$ or a similar notation) is somehow…
curious
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Are there any branches of mathematics where causality is incorporated?

Are there any branches of mathematics where causality is incorporated? For example, in Bayesian probability: $$ \ P(B|A) = \dfrac{P(A ∩ B)}{P(A)} \ $$ likewise: $$ \ P(B|A) = \dfrac{P(A | B)P(B)}{P(A)} \ $$ there doesn't seem to be a notion of time…
Alexander Mills
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Time series: ARMA characteristic polynomials have common roots

I have a question regarding the idea that if the roots of the characteristic polynomials of a time series (say some ARMA process) lie outside the unit circle, then the series will be invertible/causal (depending on which characteristic polynomial…
d89J_kl
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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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Could a continuous time-limited and absolute integrable function be the output of a causal continuous-time LTI system (Linear and Time-Invariant)??

Could a continuous time-limited and absolute integrable function be the output of a causal continuous-time Linear and Time-Invariant system (CT-LTI)?? I am trying to understand if there exists any restrictions for the derivative of a continuous and…
Joako
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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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Closed timelike curves

In a paper, I have read that the manifold $$S^1 \times \mathbb{R}^n$$ with the metric $g=-d \theta^2 +g_0$ , where $-d \theta$ is the standard metric on $S^1$ and $g_0$ is the euclidean metric on $\mathbb{R}^n$ always possesses closed causal curves.…
User1
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