Event trees are a graphical model of a set of possible situations and the
possible paths going through them, from the initial situation to the terminal
situations. With each situation, there is associated a local uncertainty model
that represents beliefs about the next situation. The uncertainty models can be
classical, precise probabilities; they can also be of a more general, imprecise
probabilistic type, in which case they can be seen as sets of classical
probabilities (yielding probability intervals). To work with such event trees,
we must combine these local uncertainty models. We show this can be done
efficiently by back-propagation through the tree, both for precise and imprecise
probabilistic models, and we illustrate this using an imprecise probabilistic
counterpart of the classical Markov chain. This allows us to perform a
robustness analysis for Markov chains very efficiently.