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#causality #statistics

The Positivity-Unconfoundedness Tradeoff

Although conditioning on more covariates could lead to a higher chance of satisfying unconfoundedness, it can lead to a higher chance of violating positivity. As we increase the dimension of the covariates, we make the subgroups for any level π‘₯ of the covariates smaller.

The Positivity-Unconfoundedness Tradeoff

This is related to the curse of dimensionality. As each subgroup gets smaller, there is a higher and higher chance that either the whole subgroup will have treatment or the whole subgroup will have control. For example, once the size of any subgroup has decreased to one, positivity is guaranteed to not hold.

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Flashcard 7070797663500

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#causality #statistics
Question
The idea is that although the treatment and potential outcomes may be unconditionally associated (due to confounding), within levels of 𝑋 , they are not associated. In other words, there is no [...-ing?] within levels of 𝑋 because controlling for 𝑋 has made the treatment groups comparable.
Answer
confounding

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an> The idea is that although the treatment and potential outcomes may be unconditionally associated (due to confounding), within levels of 𝑋 , they are not associated. In other words, there is <span>no confounding within levels of 𝑋 because controlling for 𝑋 has made the treatment groups comparable. <span>

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Flashcard 7088143207692

Question
Galois Theory Galois theory is what?
Answer
the interplay between polynomials, fields, and groups

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#causality #statistics
not only is association not causation, but causation is a sub-category of association. That’s why association and causation both flow along directed paths.
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Association flows along all unblocked paths. In causal graphs, causation flows along directed paths. Recall from Section 1.3.2 that not only is association not causation, but causation is a sub-category of association. That’s why association and causation both flow along directed paths.

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Flashcard 7088156052748

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Question
The minimal building blocks of DAGs consist of chains, forks, [...], two unconnected nodes, and two connected nodes.
Answer
immoralities

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The minimal building blocks of DAGs consist of chains, forks, immoralities, two unconnected nodes, and two connected nodes.

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Flashcard 7088157887756

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Question
The main reason for moving from exchangeability (Assumption 2.1) to conditional exchangeability (Assumption 2.2) was that it seemed like a more [...] assumption
Answer
realistic

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The main reason for moving from exchangeability (Assumption 2.1) to conditional exchangeability (Assumption 2.2) was that it seemed like a more realistic assumption

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Flashcard 7088159722764

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Question

Definition 3.4 (d-separation) Two (sets of) nodes 𝑋 and π‘Œ are d-separated by a set of nodes 𝑍 if all of the paths between (any node in) 𝑋 and (any node in) π‘Œ are [...] by 𝑍

Source: Pearl (1988), Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference

Answer
blocked

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Definition 3.4 (d-separation) Two (sets of) nodes 𝑋 and π‘Œ are d-separated by a set of nodes 𝑍 if all of the paths between (any node in) 𝑋 and (any node in) π‘Œ are blocked by 𝑍 Source: Pearl (1988), Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference

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Flashcard 7088161557772

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Question

We assumed 𝑋 is discrete when we summed over its values, but we can simply replace the sum with an [...] if 𝑋 is continuous. Throughout this book, that will be the case, so we usually won’t point it out

To jest kluczowe rΓ³wnanie.

Answer
integral

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We assumed 𝑋 is discrete when we summed over its values, but we can simply replace the sum with an integral if 𝑋 is continuous. Throughout this book, that will be the case, so we usually won’t point it out To jest kluczowe rΓ³wnanie.

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#causality #statistics

The Positivity-Unconfoundedness Tradeoff

This is related to the curse of dimensionality. As each subgroup gets smaller, there is a higher and higher chance that either the whole subgroup will have treatment or the whole subgroup will have control. For example, once the size of any subgroup has decreased to one, positivity is guaranteed to not hold.



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sfying unconfoundedness, it can lead to a higher chance of violating positivity. As we increase the dimension of the covariates, we make the subgroups for any level π‘₯ of the covariates smaller. <span>The Positivity-Unconfoundedness Tradeoff This is related to the curse of dimensionality. As each subgroup gets smaller, there is a higher and higher chance that either the whole subgroup will have treatment or the whole subgroup will have control. For example, once the size of any subgroup has decreased to one, positivity is guaranteed to not hold. <span>

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Flashcard 7088166276364

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#causality #statistics
Question
Exchangeability means that the treatment groups are exchangeable in the sense that if they were swapped, the new [...] group would observe the same outcomes as the old treatment group
Answer
treatment

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Exchangeability means that the treatment groups are exchangeable in the sense that if they were swapped, the new treatment group would observe the same outcomes as the old treatment group

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