Do we become wiser with time? On causal equivalence with tiered
  background knowledge
Christine W. Bang Vanessa Didelez
Equivalence classes of DAGs (represented by CPDAGs) may be too large to
provide useful causal information. Here, we address incorporating tiered
background knowledge yielding restricted equivalence classes represented by
'tiered MPDAGs'. Tiered knowledge leads to considerable gains in
informativeness and computational efficiency: We show that construction of
tiered MPDAGs only requires application of Meek's 1st rule, and that tiered
MPDAGs (unlike general MPDAGs) are chain graphs with chordal components. This
entails simplifications e.g. of determining valid adjustment sets for causal
effect estimation. Further, we characterise when one tiered ordering is more
informative than another, providing insights into useful aspects of background
knowledge.