Homework 4 covers the following topics:

- Markov equivalence classes (of directed acyclic graphs)
- define ‘equivalent graphs’ in terms of d-separations implied by each class of graphs

- From a set of d-separations,
- determine adjacent pairs of vertices, unshielded colliders, corresponding Markov equivalence class, CPDAG (complete partial directed acyclic graph)

- Given a joint distribution P(a,b,c,d,e) that factorizes according to an unknown DAG G* with a set of conditional independence rlationships,
- Inferring structure of DAG G*
- Assumptions on DAG G* (about inferences)

- PC algorithm
- Interpreting steps, understanding how the PC algorithm uses significance of associations to remove/direct edges
- orienting undirected edges in resulting CPDAG consistent with time-ordering of variables (common-sense causal relations)

- Single-world intervention graphs (SWIGs)
- intervene on x, read implications
- Applying the backdoor formula to adjust for confounding

- Intent-to-treat (ITT) effect of treatment assignment (Z) on outcome (Y) given treatment (X)
- Verifying IV inequalities (to verify no direct effect of treatment assignment Z on outcome Y, so only effect of treatment X influences Y)
- Constructing 3-d polytope for (%Helped, %Hurt, %Always recover, %never recover) compatible with data in Z=0 (control assignment), Z=1 (treatment assignment), and combination of both
- (recall: intersection before projection yields a subset compared to projecting THEN intersecting 3-d polytopes in 2-d)

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