Computing Inferences for Large-Scale Continuous-Time Markov Chains by Combining Lumping with Imprecision

TL;DR

This paper introduces a method for efficiently computing bounds on inferences in large-scale continuous-time Markov chains by combining state lumping with imprecise probability models, avoiding computational intractability.

Contribution

It proposes a novel approach that uses imprecise Markov chains and lumping techniques to provide guaranteed bounds on inferences in large state spaces.

Findings

Provides guaranteed lower and upper bounds for inferences.

Avoids the curse of dimensionality in large state spaces.

Enables feasible analysis of complex Markov chains.

Abstract

If the state space of a homogeneous continuous-time Markov chain is too large, making inferences - here limited to determining marginal or limit expectations - becomes computationally infeasible. Fortunately, the state space of such a chain is usually too detailed for the inferences we are interested in, in the sense that a less detailed - smaller - state space suffices to unambiguously formalise the inference. However, in general this so-called lumped state space inhibits computing exact inferences because the corresponding dynamics are unknown and/or intractable to obtain. We address this issue by considering an imprecise continuous-time Markov chain. In this way, we are able to provide guaranteed lower and upper bounds for the inferences of interest, without suffering from the curse of dimensionality.