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Flashcard 1377946963212

Tags
#consideration #contract
Question
Harris v Sheffield United FC [1988] QB 77
FACTS: To maintain law and order, a substantial police presence was required inside the defendant's football ground and this involved a significant amount of police overtime. According to the police, their attendance at the request of the club amounted to 'special police services' for which, by statute, the defendants were obliged to pay. The club refused to pay for these services claiming that the police were merely carrying out their normal public duty in ensuring the maintenance of law and order and, therefore, they had provided no consideration for the promise of the defendants to pay for those services. HELD: The responsibility of the club was [...]. The attendance of the police was necessary to assist the club in the fulfilment of this duty, which went beyond the maintenance of law and order, and for which the club should pay.
Answer
to take all reasonable steps to ensure that the game took place in conditions that did not occasion danger to any person or property

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merely carrying out their normal public duty in ensuring the maintenance of law and order and, therefore, they had provided no consideration for the promise of the defendants to pay for those services. HELD: The responsibility of the club was <span>to take all reasonable steps to ensure that the game took place in conditions that did not occasion danger to any person or property. The attendance of the police was necessary to assist the club in the fulfilment of this duty, which went beyond the maintenance of law and order, and for which the club should pay.</sp

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#causality #statistics

the fundamental problem of causal inference

It is fundamental because if we cannot observe both ๐‘Œ ๐‘– (1) and ๐‘Œ ๐‘– (0) , then we cannot observe the causal effect ๐‘Œ ๐‘– (1) โˆ’ ๐‘Œ ๐‘– (0) . This problem is unique to causal inference because, in causal inference, we care about making causal claims, which are defined in terms of potential outcomes. For contrast, consider machine learning. In machine learning, we often only care about predicting the observed outcome ๐‘Œ , so there is no need for potential outcomes, which means machine learning does not have to deal with this fundamental problem that we must deal with in causal inference.

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We get the average treatment effect (ATE) by taking an average over the ITEs: ๐œ , ๐”ผ[๐‘Œ ๐‘– (1) โˆ’ ๐‘Œ ๐‘– (0)] = ๐”ผ[๐‘Œ(1) โˆ’ ๐‘Œ(0)] , where the average is over the individuals ๐‘– if ๐‘Œ ๐‘– (๐‘ก) is deterministic. If ๐‘Œ ๐‘– (๐‘ก) is random, the average is also over any other randomness
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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. However, we often cannot know for certain if conditional exchangeability holds. There may be some unobserved confounders that are not part of ๐‘‹ , meaning conditional exchangeability is violated. Fortunately, that is not a problem in randomized experiments
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An โ€œestimatorโ€ is a function that takes a dataset as input and outputs an estimate. We discuss this statistics terminology more in Section 2.4.

Thatโ€™s the math for why we need the positivity assumption, but whatโ€™s the intuition? Well, if we have a positivity violation, that means that within some subgroup of the data, everyone always receives treatment or everyone always receives the control. It wouldnโ€™t make sense to be able to estimate a causal effect of treatment vs. control in that subgroup since we see only treatment or only control. We never see the alternative in that subgroup

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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 ๐‘ฅ 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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#causality #statistics

Assumptions of causal inference:

1. Unconfoundedness (Assumption 2.2)

2. Positivity (Assumption 2.3)

3. No interference (Assumption 2.4)

4. Consistency (Assumption 2.5)

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the main assumptions that we need for our causal graphical models to tell us how association and causation flow between variables are the following two:

1. Local Markov Assumption (Assumption 3.1)

2. Causal Edges Assumption (Assumption 3.3)

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the flow of association and causation in DAGs. We can understand this flow in general DAGs by understanding the flow in the minimal building blocks of graphs. The minimal building blocks of DAGs consist of chains (Figure 3.9a), forks (Figure 3.9b), immoralities (Figure 3.9c), two unconnected nodes (Figure 3.10), and two connected nodes (Figure 3.11)
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By โ€œflow of association,โ€ we mean whether any two nodes in a graph are associated or not associated. Another way of saying this is whether two nodes are (statistically) dependent or (statistically) independent.

Additionally, we will study whether two nodes are conditionally independent or not.

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#causality #statistics
#causality #has-images #statistics
Answer: association
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Flashcard 7071881628940

Question
โผฏๅ…ทๆ˜ฏๅปบโฝดโผฏไฝœๆต็š„ๅŸบโฝฏใ€‚้€‰ๆ‹ฉๅˆ้€‚็š„โผฏๅ…ท๏ผŒๅˆ™ๆˆไธบๆฏโผ€ไธช่ฟฝๆฑ‚ๆ•ˆ็Ž‡โฝฃๆดป็š„โผˆโผ ๆ‰€โพฏไธด็š„้—ฎ้ข˜ใ€‚้‚ฃไนˆ๏ผŒๅฆ‚ไฝ•้€‰ๆ‹ฉๅฆ‚ไฝ•้€‰ๆ‹ฉ ๅˆ้€‚็š„โผฏๅ…ทๅ‘ขๅˆ้€‚็š„โผฏๅ…ทๅ‘ข๏ผŸๆˆ‘ไปฌๅฏไปฅ้€š่ฟ‡ไธปๅฎขไฝ“็š„ๅ…ณ็ณป๏ผŒๅŽ˜ๅ‡บไธ‰ไธชๅฎžไฝ“๏ผšไฝฟโฝค่€…๏ผˆไธปไฝ“๏ผ‰ใ€โผฏๅ…ท๏ผˆๅฎขไฝ“๏ผ‰ใ€ๅฏน่ฑก๏ผˆๅฎขไฝ“๏ผ‰ไฝฟโฝค่€…๏ผˆไธปไฝ“๏ผ‰ใ€โผฏๅ…ท๏ผˆๅฎขไฝ“๏ผ‰ใ€ๅฏน่ฑก๏ผˆๅฎขไฝ“๏ผ‰ใ€‚ๅ› ๆญค๏ผŒไธ‹โพฏ ๆˆ‘ไปฌๅฐ†ไปŽ่ฟ™ไธ‰ไธชโป†ๅบฆๅˆ†ๆžๅฆ‚ไฝ•้€‰ๆ‹ฉๆ•ˆ็Ž‡โผฏๅ…ทใ€‚
Answer
[default - edit me]

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#causality #has-images #statistics
In defining the backdoor criterion (Definition 4.1) for the backdoor adjustment (Theorem 4.2), not only did we specify that the adjustment set ๐‘Š blocks all backdoor paths, but we also specified that ๐‘Š does not contain any descendants of ๐‘‡ . Why? There are two categories of things that could go wrong if we condition on descendants of ๐‘‡: 1. We block the flow of causation from ๐‘‡ to ๐‘Œ. 2. We induce non-causal association between ๐‘‡ and ๐‘Œ.
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If we condition on a descendant of ๐‘‡ that isnโ€™t a mediator, it could unblock a path from ๐‘‡ to ๐‘Œ that was blocked by a collider. For example, this is the case with conditioning on ๐‘ in Figure 4.13. This induces non-causal association between ๐‘‡ and ๐‘Œ , which biases the estimate of the causal effect. Consider the following general kind of path, where โ†’ ยท ยท ยท โ†’ denotes a directed path: ๐‘‡ โ†’ ยท ยท ยท โ†’ ๐‘ โ† ยท ยท ยท โ† ๐‘Œ . Conditioning on ๐‘ , or any descendant of ๐‘ in a path like this, will induce collider bias. That is, the causal effect estimate will be biased by the non-causal association that we induce when we condition on ๐‘ or any of its descendants (see Section 3.6).
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#causality #has-images #statistics
Unfortunately, even if we only condition on pretreatment co- variates, we can still induce collider bias. Consider what would happen if we condition on the collider ๐‘ 2 in Figure 4.16. Doing this opens up a backdoor path, along which non-causal association can flow. This is known as M-bias due to the M shape that this non-causal association flows along when the graph is drawn with children below their parents. For many examples of collider bias, see Elwert and Winship [19]
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Flashcard 7071896571148

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#causality #statistics
Question
When we say โ€œ[...],โ€ we are referring to the process of moving from a statistical estimand to an estimate
Answer
estimation

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When we say โ€œestimation,โ€ we are referring to the process of moving from a statistical estimand to an estimate

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Flashcard 7071898406156

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#causality #statistics
Question
An [...] is the quantity that we want to estimate.
Answer
estimand

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An estimand is the quantity that we want to estimate.

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SUTVA is satisfied if unit (individual) ๐‘– โ€™s outcome is simply a function of unit ๐‘– โ€™s treatment.
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#causality #statistics
The minimal building blocks of DAGs consist of chains, forks, immoralities, two unconnected nodes, and two connected nodes.
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the flow of association and causation in DAGs. We can understand this flow in general DAGs by understanding the flow in the minimal building blocks of graphs. The minimal building blocks of DAGs consist of chains (Figure 3.9a), forks (Figure 3.9b), immoralities (Figure 3.9c), two unconnected nodes (Figure 3.10), and two connected nodes (Figure 3.11)

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Flashcard 7071905746188

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#causality #statistics
Question
If two parents ๐‘‹ and ๐‘Œ share some child ๐‘ , but there is no edge connecting ๐‘‹ and ๐‘Œ , then ๐‘‹ โ†’ ๐‘ โ† ๐‘Œ is known as an [...]
Answer
immorality

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If two parents ๐‘‹ and ๐‘Œ share some child ๐‘ , but there is no edge connecting ๐‘‹ and ๐‘Œ , then ๐‘‹ โ†’ ๐‘ โ† ๐‘Œ is known as an immorality

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Flashcard 7071908105484

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#causality #statistics
Question
The Bayesian network factorization is also known as the [...] rule for Bayesian networks or Markov compatibility.
Answer
chain

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The Bayesian network factorization is also known as the chain rule for Bayesian networks or Markov compatibility.

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Flashcard 7071910464780

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#causality #statistics
Question
[...] is the assumption that the outcome we observe ๐‘Œ is actually the potential outcome under the observed treatment ๐‘‡
Answer
Consistency

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Consistency is the assumption that the outcome we observe ๐‘Œ is actually the potential outcome under the observed treatment ๐‘‡

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Flashcard 7071912299788

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#causality #has-images #statistics


Question
Well, what assumption(s) would make it so that the ATE is simply the associational difference? This is equivalent to saying โ€œwhat makes it valid to calculate the ATE by taking the average of the ๐‘Œ(0) column, ignoring the question marks, and subtracting that from the average of the ๐‘Œ(1) column, ignoring the question marks?โ€ 6 This ignoring of the question marks (missing data) is known as [...]
Answer
ignorability

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(0) column, ignoring the question marks, and subtracting that from the average of the ๐‘Œ(1) column, ignoring the question marks?โ€ 6 This ignoring of the question marks (missing data) is known as <span>ignorability <span>

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Flashcard 7071914396940

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#causality #has-images #statistics


Question
This [...] association flows along the ๐‘‡ โ† ๐‘‹ โ†’ ๐‘Œ path
Answer
non-causal

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This non-causal association flows along the ๐‘‡ โ† ๐‘‹ โ†’ ๐‘Œ path

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#causality #statistics
The potential outcomes that you do not (and cannot) observe are known as counterfactuals because they are counter to fact (reality)
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The potential outcomes that you do not (and cannot) observe are known as counterfactuals because they are counter to fact (reality). โ€œPotential outcomesโ€ are sometimes referred to as โ€œcounterfactual outcomes,โ€ but we will never do that in this book because a potential outcome ๐‘Œ(๐‘ก) does not become counter to fact unt

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#causality #statistics
An โ€œestimatorโ€ is a function that takes a dataset as input and outputs an estimate.
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An โ€œestimatorโ€ is a function that takes a dataset as input and outputs an estimate. We discuss this statistics terminology more in Section 2.4. Thatโ€™s the math for why we need the positivity assumption, but whatโ€™s the intuition? Well, if we have a positivity violation,

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Flashcard 7071920688396

Tags
#causality #statistics
Question

The Fundamental Problem of Causal Inference:

It is impossible to observe all potential outcomes for a given [...]

Answer
individual

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The Fundamental Problem of Causal Inference: It is impossible to observe all potential outcomes for a given individual

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Flashcard 7071922523404

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#causality #statistics
Question
[...] is the main assumption necessary for causal inference. Armed with this assumption, we can identify the causal effect within levels of ๐‘‹
Answer
Conditional exchangeability

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Conditional exchangeability is the main assumption necessary for causal inference. Armed with this assumption, we can identify the causal effect within levels of ๐‘‹

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#causality #statistics
The Positivity-Unconfoundedness Tradeoff
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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 dimensi

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#causality #statistics
In machine learning, we often only care about predicting the observed outcome ๐‘Œ , so there is no need for potential outcomes, which means machine learning does not have to deal with this fundamental problem that we must deal with in causal inference
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the fundamental problem of causal inference

It is fundamental because if we cannot observe both ๐‘Œ ๐‘– (1) and ๐‘Œ ๐‘– (0) , then we cannot observe the causal effect ๐‘Œ ๐‘– (1) โˆ’ ๐‘Œ ๐‘– (0) .

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#causality #statistics
To identify a causal effect is to reduce a causal expression to a purely statistical expression.
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To identify a causal effect is to reduce a causal expression to a purely statistical expression. In this chapter, that means to reduce an expression from one that uses potential outcome notation to one that uses only statistical notation such as ๐‘‡ , ๐‘‹ , ๐‘Œ , expectations, and condit

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Flashcard 7071934319884

Tags
#causality #statistics
Question
To [...] a causal effect is to reduce a causal expression to a purely statistical expression.
Answer
identify

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To identify a causal effect is to reduce a causal expression to a purely statistical expression.

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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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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. However, we often cannot know for certain if conditional exchangeability holds. There may be some unobserved confounders that are not part of ๐‘‹ , meaning conditional exchangeability is

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Flashcard 7071938776332

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#causality #statistics
Question
there is no reason to expect that the groups are the same in all relevant variables other than the treatment. However, if we control for relevant variables by conditioning, then maybe the subgroups will be [...]. We will clarify what the โ€œrelevant variablesโ€ are in Chapter 3,
Answer
exchangeable

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reason to expect that the groups are the same in all relevant variables other than the treatment. However, if we control for relevant variables by conditioning, then maybe the subgroups will be <span>exchangeable. We will clarify what the โ€œrelevant variablesโ€ are in Chapter 3, <span>

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Flashcard 7071941659916

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#causality #statistics
Question

Assumption 3.2 ([...] Assumption)

1. Given its parents in the DAG, a node ๐‘‹ is independent of all its non-descendants (Assumption 3.1).

2. Adjacent nodes in the DAG are dependent.

Answer
Minimality

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Assumption 3.2 (Minimality Assumption) 1. Given its parents in the DAG, a node ๐‘‹ is independent of all its non-descendants (Assumption 3.1). 2. Adjacent nodes in the DAG are dependent.

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Flashcard 7071945329932

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#causality #statistics

Question
Answer: [...]
Answer
association

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Answer: association

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Flashcard 7071947164940

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#causality #statistics
Question
An estimate (noun) is an approximation of some [...], which we get using data
Answer
estimand

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An estimate (noun) is an approximation of some estimand, which we get using data

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Flashcard 7071949262092

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#causality #statistics
Question

Assumption 3.1 ([...] Assumption)

Given its parents in the DAG, a node ๐‘‹ is independent of all its non-descendants

Answer
Local Markov

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Assumption 3.1 (Local Markov Assumption) Given its parents in the DAG, a node ๐‘‹ is independent of all its non-descendants

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#causality #statistics
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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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, and the new control group would observe the same outcomes as the old control group.

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Flashcard 7071952669964

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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 [...] group
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old 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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Flashcard 7071954504972

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The idea is that although the treatment and potential outcomes may be unconditionally associated (due to confounding), within levels of ๐‘‹ , they are not associated. In other words, there is no confounding within levels of ๐‘‹ because controlling for ๐‘‹ has made the treatment groups [...].
Answer
comparable

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associated (due to confounding), within levels of ๐‘‹ , they are not associated. In other words, there is no confounding within levels of ๐‘‹ because controlling for ๐‘‹ has made the treatment groups <span>comparable. <span>

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We do not have exchangeability in the data because ๐‘‹ is a common cause of ๐‘‡ and ๐‘Œ
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No interference means that my outcome is unaffected by anyone elseโ€™s treatment.
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No interference means that my outcome is unaffected by anyone elseโ€™s treatment. Rather, my outcome is only a function of my own treatment. Weโ€™ve been using this assumption implicitly throughout this chapter. Weโ€™ll now formalize it. Assumption 2.4 (No Interference)

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Flashcard 7071959747852

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No interference means that my outcome is unaffected by anyone elseโ€™s [...].
Answer
treatment

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No interference means that my outcome is unaffected by anyone elseโ€™s treatment.

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By โ€œflow of association,โ€ we mean whether any two nodes in a graph are associated or not associated. Another way of saying this is whether two nodes are (statistically) dependent or (statistically) independent.
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By โ€œflow of association,โ€ we mean whether any two nodes in a graph are associated or not associated. Another way of saying this is whether two nodes are (statistically) dependent or (statistically) independent. Additionally, we will study whether two nodes are conditionally independent or not.

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Flashcard 7071964204300

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It turns out that much of the work for causal graphical models was done in the field of probabilistic graphical models. Probabilistic graphical models are [...] models while causal graphical models are causal models.
Answer
statistical

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It turns out that much of the work for causal graphical models was done in the field of probabilistic graphical models. Probabilistic graphical models are statistical models while causal graphical models are causal models.

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Flashcard 7071966825740

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Assumptions of causal inference:

1. [...] (Assumption 2.2)

2. Positivity (Assumption 2.3)

3. No interference (Assumption 2.4)

4. Consistency (Assumption 2.5)

Answer
Unconfoundedness

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Assumptions of causal inference: 1. Unconfoundedness (Assumption 2.2) 2. Positivity (Assumption 2.3) 3. No interference (Assumption 2.4) 4. Consistency (Assumption 2.5)

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We denote by ๐‘Œ(1) the potential outcome of happiness you would observe if you were to get a dog ( ๐‘‡ = 1 ). Similarly, we denote by ๐‘Œ(0) the potential outcome of happiness you would observe if you were to not get a dog ( ๐‘‡ = 0 )
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More generally, the potential outcome ๐‘Œ(๐‘ก) denotes what your outcome would be, if you were to take treatment ๐‘ก
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Flashcard 7071972592908

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We will take this table as the whole population of interest. Because of the fundamental problem of causal inference, this is fundamentally a [...] problem. All of the question marks in the table indicate that we do not observe that cell.
Answer
missing data

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We will take this table as the whole population of interest. Because of the fundamental problem of causal inference, this is fundamentally a missing data problem. All of the question marks in the table indicate that we do not observe that cell.

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Flashcard 7071974690060

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We have seen that [assumption?] is extremely important (Equation 2.3), but how realistic of an assumption is it? In general, it is completely unrealistic because there is likely to be confounding in most data we observe (causal structure shown in Figure 2.1). However, we can make this assumption realistic by running randomized experiments, which force the treatment to not be caused by anything but a coin toss, so then we have the causal structure shown in Figure 2.2. We cover randomized experiments in greater depth in Chapter 5.
Answer
ignorability

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We have seen that ignorability is extremely important (Equation 2.3), but how realistic of an assumption is it? In general, it is completely unrealistic because there is likely to be confounding in most data we obser

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Flashcard 7071977311500

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Positivity is the condition that all subgroups of the data with different covariates have [...] probability of receiving any value of treatment
Answer
some

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Positivity is the condition that all subgroups of the data with different covariates have some probability of receiving any value of treatment

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Flashcard 7071979146508

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The idea is that although the treatment and potential outcomes may be unconditionally associated (due to confounding), [...] levels of ๐‘‹ , they are not associated
Answer
within

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The idea is that although the treatment and potential outcomes may be unconditionally associated (due to confounding), within levels of ๐‘‹ , they are not associated

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Flashcard 7071982292236

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We get the [...] (ATE) by taking an average over the ITEs: ๐œ , ๐”ผ[๐‘Œ ๐‘– (1) โˆ’ ๐‘Œ ๐‘– (0)] = ๐”ผ[๐‘Œ(1) โˆ’ ๐‘Œ(0)] , where the average is over the individuals ๐‘– if ๐‘Œ ๐‘– (๐‘ก) is deterministic. If ๐‘Œ ๐‘– (๐‘ก) is random, the average is also over any other randomness
Answer
average treatment effect

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We get the average treatment effect (ATE) by taking an average over the ITEs: ๐œ , ๐”ผ[๐‘Œ ๐‘– (1) โˆ’ ๐‘Œ ๐‘– (0)] = ๐”ผ[๐‘Œ(1) โˆ’ ๐‘Œ(0)] , where the average is over the individuals ๐‘– if ๐‘Œ ๐‘– (๐‘ก) is deterministic. If ๐‘Œ ๐‘– (๐‘ก) is random, the

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