Factual condition

As explained in Causal AI

A factual condition is an observed fact, event, or piece of evidence that restricts the population or scope described by a conditional query.

A factual condition is an observed fact, event, or piece of evidence that narrows the population under discussion. In P(Y | X = x), the factual condition appears after the vertical bar and filters attention to cases where X actually equals x. section 8.2.2

Keep factual conditions distinct from hypothetical conditions:

• A factual query asks what Y is for cases where X = x: P(Y | X = x). section 8.2.3
• A hypothetical query asks what Y would be if X were set to x, regardless of its observed causes. section 8.2.3
• The two can combine: ask a hypothetical question about a population already filtered by a factual condition. section 8.2.3

Game-player example

“What would in-game purchases be for players with high side-quest engagement?” uses high engagement as a factual condition. A counterfactual instead asks what purchases would be if engagement were high for a player whose observed engagement was low; the low engagement remains the factual condition. section 8.2.2 section 8.2.4

Factual and hypothetical conditions may conflict, producing a counterfactual query. When they agree, the consistency rule removes the redundant hypothetical condition: P(YX=x | X=x, Z=z) = P(Y | X=x, Z=z). section 8.2.4 section 8.2.5

Figure 8.4 Elements of a conditional counterfactual hypothetical formalized in counterfactual notation

Use the notation diagram to locate factual conditions and distinguish them from hypothetical conditions in conditional counterfactual queries. section 8.2.4

How Causal AI covers it

How deep it goes

Defines the notation, contrasts factual and hypothetical conditions, and applies consistency but does not develop estimation procedures.

Examples

Uses player engagement and in-game purchases to contrast population filtering, intervention questions, and conflicting observed outcomes.

What it assumes

Assumes conditional probability notation and develops the distinction between observed filtering and hypothetical intervention.

What you can do after

Evaluate/understand whether a query describes observed subpopulations, hypothetical interventions, or counterfactual conflicts.

How it connects

Connects factual conditions to conditional probability, conditional hypotheticals, interventions, counterfactuals, and the consistency rule.

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Related concepts

• conditional probabilitypart of · Conditional probability is the probability of an event or variable value given that specified information, an event, or another variable’s value is known.
• hypothetical conditioncontrasts with · A hypothetical condition is an alternative value or circumstance imposed or considered in a counterfactual analysis.
• conditional hypotheticalcontrasts with · A conditional hypothetical is a query about an outcome under a specified condition without requiring that the condition replace an observed cause in the same individual.

This explainer was generated by Manning's knowledge graph from the text of Causal AI. The section links point to the parts of the book it draws on.