[Probability] Inference

Types of inference

Diagnostic reasoning: to infer causes from effects
ex) P(B=1|M=1), given B–>A–>M

Causal reasoning: from causes to effects
ex) P(M=1|B=1), given B–>A–>M

Explaining away: about competing/multiple causes
ex) P(E=1|J=1,B=1) < P(E=1|J=1), given B,E–>A–>J,M

* Earthquake being true would be less likely when you already know that Burglary was what may have caused John to call.
* “Explaining away” is a common pattern of reasoning in which confirmation of one cause reduces the need to invoke other causes

Mixing causes/effects: P(B=1,M=1|A=1,E=1)

Strategy for inference

Bayes rule: express P(Q|E) in terms of conditional probabilities that respect DAG ordering

Product rule: express joint predictions in terms of individual predictions

Marginalization: introduce nodes so that we predict children from parents

Marginal or conditional independence: use to remove terms on RHS of conditioning bar

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