Uncertainty Quantification for Markov Processes via Variational Principles and Functional Inequalities
Year: 2020
Type: article
Abstract: Information-theory based variational principles have proven effective at providing scalable uncertainty quantification (i.e., robustness) bounds for quantities of interest in the presence of nonparametric model-form uncertainty. In this work, we combine such variational formulas with functional inequalities (Poincaré, $\log$-Sobolev, Liapunov functions) to derive explicit uncertainty quantification bounds for time-averaged observables, comparing a Markov process to a second (not necessarily Markov) process. These bounds are well behaved in the infinite-time limit and apply to steady-states of both discrete and continuous-time Markov processes.
DOI: 10.1137/19m1237429
Authors: Jeremiah Birrell, Luc Rey-Bellet
Language: English
Subfield: Statistics, Probability and Uncertainty
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
Awards: G2416061413, G5435160259
OpenAlex ID: W2903832574