Path-space information bounds for uncertainty quantification and sensitivity analysis of stochastic dynamics

TL;DR

This paper introduces new bounds for uncertainty quantification and sensitivity analysis in stochastic dynamics, utilizing path-space information measures that are computationally efficient and applicable to high-dimensional systems.

Contribution

It develops tight, goal-oriented divergence bounds for path observables and sensitivity bounds based on the path Fisher Information Matrix, enabling gradient-free analysis in complex stochastic models.

Findings

Bounds depend on observable variance and are Monte Carlo computable.

Sensitivity bounds rely on local dynamics, avoiding gradient calculations.

Applicable to high-dimensional systems like reaction networks and molecular simulations.

Abstract

Uncertainty quantification is a primary challenge for reliable modeling and simulation of complex stochastic dynamics. Such problems are typically plagued with incomplete information that may enter as uncertainty in the model parameters, or even in the model itself. Furthermore, due to their dynamic nature, we need to assess the impact of these uncertainties on the transient and long-time behavior of the stochastic models and derive corresponding uncertainty bounds for observables of interest. A special class of such challenges is parametric uncertainties in the model and in particular sensitivity analysis along with the corresponding sensitivity bounds for stochastic dynamics. Moreover, sensitivity analysis can be further complicated in models with a high number of parameters that render straightforward approaches, such as gradient methods, impractical. In this paper, we derive uncertainty and sensitivity bounds for path-space observables of stochastic dynamics in terms of new goal-oriented divergences; the latter incorporate both observables and information theory objects such as the relative entropy rate. These bounds are tight, depend on the variance of the particular observable and are computable through Monte Carlo simulation. In the case of sensitivity analysis, the derived sensitivity bounds rely on the path Fisher Information Matrix, hence they depend only on local dynamics and are gradient-free. These features allow for computationally efficient implementation in systems with a high number of parameters, e.g., complex reaction networks and molecular simulations.