To address this, we can sample a state-conditional distribution over child lists λ k from a DP with L k as a base measure.
we augment the basic model given in the previous section with the variables ζ, L k , and λ k : c t |λ k ∼ λ k An important consequence of defining L k locally (instead of globally, using β instead of the π k s) is that the model captures not only what sequences of children a state prefers, but also the individual children that state prefers; if a state gives high probability to some particular sequence of children, then it is likely to also give high probability to other sequences containing those same states, or a subset thereof.