Affine arithmetic for assessing the uncertainty propagation on steady-state probabilities of Markov models owing to uncertainties in transition rates

Abstract

This article proposes the use of affine arithmetic as an alternative approach for assessing the effects of uncertainties of transition rates on the steady-state probabilities for each possible state of a system represented by a Markov model. Affine arithmetic is an extension of interval arithmetic, able to track “the dependency between variables throughout calculations” and to provide strict bounds. Several examples illustrate the proposed approach. Results are compared with other approaches, such as interval arithmetic, Monte Carlo simulation or solving linear systems of simultaneous equations.