# Publications

## Extending the domain of imprecise jump processes from simple variables to measurable ones Ghent University

We extend the domain of imprecise jump processes, also known as imprecise continuous-time Markov chains, from inferences that depend on a finite number of time points to inferences that can depend on the state of the system at all time points. We also investigate the continuity properties of the resulting lower and upper expectations with respect to point-wise convergent sequences that are monotone or dominated. For two particular inferences, ...

## Sum-product laws and efficient algorithms for imprecise Markov chains Ghent University

We propose two sum-product laws for imprecise Markov chains, and use these laws to derive two algorithms to efficiently compute lower and upper expectations for imprecise Markov chains under complete independence and epistemic irrelevance. These algorithms work for inferences that have a corresponding sum-product decomposition, and we argue that many well-known inferences fit their scope. We illustrate our results on a simple epidemiological ...

## A graphical study of comparative probabilities Ghent University

We consider a set of comparative probability judgements over a finite possibility space and study the structure of the set of probability measures that are compatible with them. We relate the existence of some compatible probability measure to WalleyU+2019s behavioural theory of imprecise probabilities, and introduce a graphical representation that allows us to bound, and in some cases determine, the extreme points of the set of compatible ...

## An imprecise probabilistic estimator for the transition rate matrix of a continuous-time Markov Chain Ghent University

We consider the problem of estimating the transition rate matrix of a continuous-time Markov chain from a finite-duration realisation of this process. We approach this problem in an imprecise probabilistic framework, using a set of prior distributions on the unknown transition rate matrix. The resulting estimator is a set of transition rate matrices that, for reasons of conjugacy, is easy to find. To determine the hyperparameters for our set of ...

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

If the state space of a homogeneous continuous-time Markov chain is too large, making inferencesU+2014here limited to determining marginal or limit expectationsU+2014becomes 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 detailedU+2014smallerU+2014state space suffices to unambiguously formalise the inference. However, in general ...

## First steps towards an imprecise Poisson process Ghent University

The Poisson process is the most elementary continuous-time stochastic process that models a stream of repeating events. It is uniquely characterised by a single parameter called the rate. Instead of a single value for this rate, we here consider a rate interval and let it characterise two nested sets of stochastic processes. We call these two sets of stochastic process imprecise Poisson processes, explain why this is justified, and study the ...

## Optimal control of a linear system subject to partially specified input noise Ghent University

One of the most basic problems in control theory is that of controlling a discrete-time linear system subject to uncertain noise with the objective of minimising the expectation of a quadratic cost. If one assumes the noise to be white, then solving this problem is relatively straightforward. However, white noise is arguably unrealistic: noise is not necessarily independent and one does not always precisely know its expectation. We first recall ...

## Bounding inferences for large-scale continuous-time Markov chains : a new approach based on lumping and imprecise Markov chains Ghent University

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 detailedU+2014smallerU+2014state space suffices to unambiguously formalise the inference. However, in general this so-called lumped state space inhibits computing exact inferences ...