  We study multistage distributionally robust optimization (DRO) to hedge
against ambiguity in quantifying the underlying uncertainty of a problem.
Recognizing that not all the realizations and scenario paths might have an
"effect" on the optimal value, we investigate the question of how to define and
identify critical scenarios for nested multistage DRO problems. Our analysis
extends the work of Rahimian, Bayraksan, and Homem-de-Mello [Math. Program.
173(1--2): 393--430, 2019], which was in the context of a static/two-stage
setting, to the multistage setting. To this end, we define the notions of
effectiveness of scenario paths and the conditional effectiveness of
realizations along a scenario path for a general class of multistage DRO
problems. We then propose easy-to-check conditions to identify the
effectiveness of scenario paths in the multistage setting when the
distributional ambiguity is modeled via the total variation distance. Numerical
results show that these notions provide useful insight on the underlying
uncertainty of the problem.
