Questions tagged [d-separation]

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Deriving conditional independence statements for causal graphs with selection nodes

In "basic" causal graphs / DAGs / probabilistic graphical models (PGMs), conditional independence statements can be derived using the d-separation criterion. How does this work if selection ...
Eike P.'s user avatar
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The use of p-values in tests of d-separation

In his very helpful online book on structural equation modeling, Jon Lefcheck writes the following concerning d-separation tests for SEMs: Once the model is fit, statistical independence is assessed ...
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Why is d-separation only for disjoint sets?

I'm reading Molak's Causal Inference and Discovery in Python: Unlock the secrets of modern causal machine learning with DoWhy, EconML, PyTorch and more and I made note that I've taken the ...
Galen's user avatar
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Markov and Faithfullness Condition in disconnected DAG/Bayesian network

I'm very confused about the Markov- and the faithfulness condition in disconnected DAGs, as I've never seen such examples. Assume for example I had a DAG where X -> Y, Z. Thus, Z is disconnected ...
Mika2019's user avatar
6 votes
1 answer
187 views

Causal inference and the backdoor-criterion

I am trying to determine if the authors of the following report missed out on an important factor or if i am the one who have missed out on something. In the following report: Bias Correction For Paid ...
max's user avatar
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1 answer
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Invalid Adjustment Sets in causal graph

I'm reading a documentation on causal inference on graph and I'm currently on the chapter about identification. In this section, the authors give examples of invalid adjustment sets, one of which is ...
statslearner's user avatar
1 vote
0 answers
148 views

Shipley's d separation test in piecewise structural equation model

I have created a piecewise structural equation model for when the temperature exceeds 0 degrees Celsius, and how that relates to the green up day across Northern Europe. I have standardised all data <...
Thomas's user avatar
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1 answer
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Meaning of $\uparrow$ in below d-separation algorithm from Koller

In Probabilistic Graphical Models by Koller and Friedman there is an algorithm to find the nodes reachable from node $X$ via trails that are active, given conditioning set $Z$. What is the meaning of &...
Anirban Chakraborty's user avatar
4 votes
1 answer
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sigma-separation question in cyclic causal graph - understanding sigma-separation

Main Question In https://arxiv.org/pdf/1807.03024.pdf, a generalization of d-separation in DAGs is introduced, called $\sigma$-separation for cyclic graphs. I am wondering how $v_1 \perp v_6$ using ...
ajl123's user avatar
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1 answer
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What will happen if we condition on the parent of a confounder?

Say we have a confounder $U$ between $X$ and $Y$, i.e. graphically, $U\rightarrow X$ and $U \rightarrow Y$, $X$ and $Y$ are not directly connected. According to the d-seperation rule, I know ...
Mingzhou Liu's user avatar
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Not necessarily conditionally independent = dependent?

After concluding the d-separation procedure (ancestral graph -> moral graph -> removing directed links), I am left with two nodes that are connected and a conclusion that they are "not ...
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D separation from Spirtes paper

Hi, i've been trying to learn d-separation and came across this figure in figure 4 (page 9) of Spirtes paper and i am a bit confuse. In the paper, Spirtes says X4 is not d-separated from X1 given ...
Alim's user avatar
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Conditional independence tests not respecting d-separation

Wrong example, please refer to the second example I just tried to model a Bayesian network composed of 3 variables as follows $A\sim N(0,1)$ $B\sim A + N(0,1)$ $T\sim A + B + N(0,1)$ In the DAG ...
DaSim's user avatar
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2 answers
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Why are $X$ and $Y$ in this graph d-separated given $Z_2$?

I am learning the book "Causality" by Judea Pearl. In Chapter 1, page 18, the d-separation examples, there is a thing I do not understand. Consider this graph (a) on Page 18: It says that $...
Minh-Long Luu's user avatar
4 votes
1 answer
190 views

Spirtes' example of d-separation not leading to independence in a directed cyclic graph with non-linear structural equations

In Spirtes (1995) there is an example (Fig. 4 on page 495, reproduced below) of a directed cyclic graph with non-linear structural equations in which $d$-separation of $X$ and $Y$ given $\{Z, W\}$ ...
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d-separation and implication of its theorem

Let $(X\perp Y | Z)_P$ represents the conditional independence of X and Y separated by Z. I am very confused about the following theorem about d-separation from Judea Pearl's text which says the ...
Dan's user avatar
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Causality: Implication of d-separation

I am confused about the following theorem about d-separations from Judea Pearl's causality textbook which reads as follow: "If sets X and Y are d-separated by Z in a DAG G, then X is independent of Y ...
Dan's user avatar
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5 votes
1 answer
146 views

Causality: Models, Reasoning, and Inference: Diagram Question

I am self-studying Causality: Models, Reasoning, and Inference, by Judea Pearl, and there is a question I am particularly stumped on. It reads like this: Problem Statement: Given this fragment of a ...
Adrian Keister's user avatar