# Quantification of Model Uncertainty on Path-Space via Goal-Oriented Relative Entropy

## TL;DR

This paper extends the use of relative entropy rate for quantifying uncertainty in stochastic models, providing tighter bounds for a broader class of path-space quantities like hitting times and discounted observables.

## Contribution

It introduces new information-theoretic objects for path-space quantities and develops corresponding uncertainty quantification bounds that improve upon previous methods.

## Key findings

- Tighter UQ bounds for ergodic averages and other path-space quantities.
- Applicable to diverse stochastic models including diffusion processes and queueing models.
- Enhanced methods for uncertainty quantification in stochastic modeling.

## Abstract

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.