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

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.Comment: 9th International Conference on Soft Methods in Probability and Statistics (SMPS 2018

Simulation study of large production network robustness in uncertain environment

Robustness is an important success factor for production networks in which the operation of enterprises is subjected to an uncertain environment. In this paper, the robustness of networks is studied as a function of network size. The study is performed through a simulation experiment in which the uncertain environment is modelled by introducing perturbations in demand. The decision-making model mimics the behaviour of socially connected human subjects. The results show how robustness and production rate are affected by system size and social network structure, and how this is relevant for the design and operation of future manufacturing systems.This work was partially supported by the Portuguese National Funding Agency for Science, Research and Technology (FCT), Grant No. UID/CEC/00319/2013, and by the Slovenian Research Agency, Grant No. P2-0270.info:eu-repo/semantics/publishedVersio

Computing inferences for large-scale continuous-time Markov chains by combining lumping with imprecision

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

A continuous updating rule for imprecise probabilities

The paper studies the continuity of rules for updating imprecise probability models when new data are observed. Discontinuities can lead to robustness issues: this is the case for the usual updating rules of the theory of imprecise probabilities. An alternative, continuous updating rule is introduced. © Springer International Publishing Switzerland 2014

Probabilistic Model Checking of Biological Systems with Uncertain Kinetic Rates

Abstract. We present an abstraction of the probabilistic semantics of Multiset Rewriting to formally express systems of reactions with uncertain kinetic rates. This allows biological systems modelling when the exact rates are not known, but are supposed to lie in some intervals. On these (abstract) models we perform probabilistic model checking obtaining lower and upper bounds for the probabilities of reaching states satisfying given properties. These bounds are under- and overapproximations, respectively, of the probabilities one would obtain by verifying the models with exact kinetic rates belonging to the intervals. Key words: probabilistic model checking, systems biology, uncertain kinetic rates, abstract interpretation, interval Markov chains.