Alexander Erreygers

Bounding inferences for large-scale continuous-time Markov chains: A new approach based on lumping and imprecise Markov chains

Alexander Erreygers & Jasper De Bock

In International Journal of Approximate Reasoning, 115:96–133, Dec. 2019.

If the state space of a homogeneous continuous-time Markov chain is too large, making inferences 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.