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In contrast, the non-strict causal edges assumption would allow for some parents to not be causes of their children. It would just assume that children are not causes of their parents. This allows us to draw graph

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ion 4.1) for the backdoor adjustment (Theorem 4.2), not only did we specify that the adjustment set π blocks all backdoor paths, but we also specified that π does not contain any descendants of <span>π <span>

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the local Markov assumption is, it only gives us information about the independencies in π that a DAG implies. It does not even tell us that if π and π are adjacent in the DAG, then π and π are <span>dependent. And this additional information is very commonly assumed in causal DAGs. To get this guaranteed dependence between adjacent nodes, we will generally assume a slightly stronger assumpti

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An βestimatorβ is a function that takes a dataset as input and outputs an estimate. We discuss this statistics terminology more in Section 2.4. Thatβs the math for why we need the positivity assumption, but whatβs 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 wouldnβt 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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red to as βcounterfactual outcomes,β but we will never do that in this book because a potential outcome π(π‘) does not become counter to fact until another potential outcome π(π‘ 0 ) is observed. <span>The potential outcome that is observed is sometimes referred to as a factual. Note that there are no counterfactuals or factuals until the outcome is observed. Before that, there are only potential outcomes <span>

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Consistency is the assumption that the outcome we observe π is actually the potential outcome under the observed treatment π

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The flow of association is symmetric, whereas the flow of causation is not.

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t uses potential outcome notation to one that uses only statistical notation such as π , π , π , expectations, and conditioning. This means that we can calculate the causal effect from just the <span>observational distribution π(π, π, π) <span>

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When we say βestimation,β we are referring to the process of moving from a statistical estimand to an estimate

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Answer: conditional association

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Example of not blocked the path A - Y

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in 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. <span>Causal Edges Assumption (Assumption 3.3) <span>

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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 π

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An βestimatorβ is a function that takes a dataset as input and outputs an estimate.

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A potential outcome π(π‘) is distinct from the observed outcome π in that not all potential outcomes are observed

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the fundamental problem of causal inference It is fundamental because if we cannot observe both π π (1) and π π (0) , then we cannot observe the causal effect π π (1) β π π (0) .

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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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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.

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For example, if we remove the π΄ β π΅ to get Figure 3.5, then π΄ β πΆ β π΅ is an immorality