  Quantifying the impact of parametric and model-form uncertainty on the
predictions of stochastic models is a key challenge in many applications.
Previous work has shown that the relative entropy rate is an effective tool for
deriving path-space uncertainty quantification (UQ) bounds on ergodic averages.
In this work we identify appropriate information-theoretic objects for a wider
range of quantities of interest on path-space, such as hitting times and
exponentially discounted observables, and develop the corresponding UQ bounds.
In addition, our method yields tighter UQ bounds, even in cases where previous
relative-entropy-based methods also apply, e.g., for ergodic averages. We
illustrate these results with examples from option pricing, non-reversible
diffusion processes, stochastic control, semi-Markov queueing models, and
expectations and distributions of hitting times.
