# 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 ...
• 2,908
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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 ...
• 349
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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 ...
• 8,185
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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 ...
• 11
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### 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 ...
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1 vote
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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 ...
1 vote
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 <...
• 528
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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 &...
193 views

### 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 ...
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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 ...
• 371
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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 ...
1 vote
67 views

### 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 ...
• 11
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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 ...
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1 vote
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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 ...
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