Title Promoter Affiliations Abstract "Imprecise random sequences and their statistical estimation" "Jasper De Bock" "Department of Electronics and information systems" "That scientific modelling should aim to take into account uncertainty, is by now widely accepted. To that end, most scholars use probabilities to describe this uncertainty. However, it has been convincingly argued that there are cases in which this is not defendable. If these probabilities are to be used for high-risk decision making under uncertainty, as for example required in medical diagnosis and self-driving cars, this problem cannot be neglected. To better understand the problem, consider a sequence of binary data, consisting of zeros and ones, for example obtained through physical experiments. If one associates a probability with this data sequence, this implies that it should adhere to probabilistic laws, the convergence of relative frequencies being a prime example. However, there are plenty of binary data sequences for which the relative frequency of ones does not converge at all. Fortunately, these kinds of limitations can be addressed by using probability intervals instead of probabilities, which will then for example provide lower and upper bounds on non-stabilising frequencies. The aim of this proposal is to develop a methodology able to do this in general contexts. The first part consists in further developing notions of imprecise randomness that are able to associate appropriate intervals with infinite sequences of data. The second part consists in developing efficient statistical methods for learning these intervals." "Towards a more robust treatment of discrete-time stochastic processes: developing a theoretical framework for working with imprecise probabilities in Markov chains" "Gert De Cooman" "Department of Electronics and information systems" "We aim to develop a theoretical framework, and efficient algorithms, for imprecise discrete-time Markov chains. The imprecision relates to the parameters of the model, which need not be specified exactly. This leads to more robust and reliable results. The motivation stems from the popularity of traditional Markov chains, and from society’s increasing demand for features such as robustness and reliability." "Imprecise continuous-time Markov chains" "Aleksandra Pizurica" "Department of Telecommunications and information processing, Department of Electronics and information systems" "We aim to develop a theoretical framework, and efficient algorithms, for imprecise continuous-time Markov chains. The imprecision relates to the parameters of the model, which need not be specified exactly. This leads to more robust and reliable results. The motivation stems from the popularity of traditional Markov chains, and from societyU+2019s increasing demand for features such as robustness and reliability." "Efficient inference in large-scale queueing models using imprecise continuous-time Markov chains" "Jasper De Bock" "Department of Electronics and information systems" "A continuous-time Markov chain is a probabilistic model that is successful at describing the uncertain time evolution of various systems. Since it is also quite simple to make predictions about its future behaviour, it has become a very popular tool in a large range of applied domains, including engineering, artificial intelligence, mathematical finance, bio-informatics and queueing. However, when the dimensions of the model are too large, computations become intractable to perform. This limits its practical use to applications of a limited scale. During the last year, it has been discovered that this problem can be solved by using an imprecise continuous-time Markov chain. Simply put, this is a specific collection of smaller models whose common conclusions are guaranteed to be compatible with the original large-scale model. By performing computations for all of these smaller models simultaneously, it becomes feasible to compute reliable inferences for large-scale models. Unfortunately, imprecise continuous-time Markov chains are not yet sufficiently developed to be able to fully exploit this discovery. In particular, performing computations with them is currently only feasible for a fairly limited class of inferences. This project aims to develop the required mathematical and algorithmic foundations for dealing with the more advanced inferences that are typically needed in practical applications, and to apply them to large-scale queueing models." "Robust modelling and optimisation of stochastic processes with imprecise probabilities, applied to queueing systems" "Stijn De Vuyst" "Department of Industrial Systems Engineering and Product Design" "In this project the paradigm of impreciseprobabilities (expertise 1st promotor) is applied to stochastic processes that are usually described by ‘common’, i.e. precise, probability theory. Thetargeted application is on processes that occur in queueing systems (expertise of 2nd and 3rd promotor). The new treatment allows us to quantify the belief we can put in results from classic queueing analysis in the presence of model uncertainty." "Imprecise Mental Number Representations And Decision Making under Risk." "Ferdinand Vieider" "Department of Economics" "Traditional decision theory assumes that people use precise representations of involved probabilities and outcomes to evaluate options, but observed behavior seems much less precise. Khaw et al. (2020) take an essential step by introducing imprecision into modeling decision-making. Specifically, their model assumes that people mentally form imprecise representations of numerosity after seeing a number, and such inexact number representations result in small-stake risk aversion and stochastic choices simultaneously. This project aims to provide empirical evidence for this model. Package 1 adopts cognitive load manipulation, designed to occupy subjects' cognitive resources and thus make their number representations noisier, to test whether treated subjects' choices become more risk-averse and random. Related studies show that the acuity of mental number representations is determined by approximate numeracy, a numerical competence that contains two separate elements. Package 2 randomly assigns two treatments (brain stimulation and brain training) to subjects to enhance these two elements respectively and then tests the hypothesis that the treated subjects should behave more risk-neutrally and consistently while further comparing the relative role of these two elements of approximate numeracy in decision-making. Finally, Package 3 studies whether and how noisy number representations lead to violations of stochastic dominance and tests two treatments' effects on the violations." "Imprecise random sequences and their statistical estimation." "Jasper De Bock" "Department of Electronics and information systems" "We aim to develop a new framework for describing and estimating the uncertainty that is associated with data sequences. Our goals are similar to those of traditional statistics, but the crucial difference is that we intend to do drop the restrictive assumption that uncertainty should be described by a probability measure, resulting in methods that are more reliable and robust." "Robust modelling and optimisation in stochastic processes using impreciseprobabilities, with applications to queueing" "Department of Industrial Systems Engineering and Product Design, Department of Telecommunications and information processing" "A process is called stochastic when its time-evolution is to someextent uncertain. To model and reason with such uncertainty, weuse methods from probability theory. This allows us to analyse thebehaviour of these processes, and to design or influence them inorder to make their behaviour optimal or desirable.One crucial problem is that most often we are not only uncertainabout the processes themselves, but also about the validity of theprobabilistic models we use for studying them. The theory ofimprecise probability is a recent development of probability theorythat is designed to dealing with this so-called model uncertainty ina robust way.The project aims first of all at further developing this generaltheory, all the while concentrating on techniques that are usefulfor, and tailored towards, working with stochastic processes. Atthe same time, we will apply and evaluate the developed methodsand techniques in the practically important area of queueingapplications for communication systems.The project brings together two research groups at Ghent University:SYSTeMS, whose expertise lies in robust uncertainty modellingusing imprecise probabilities, and SMACS, who are focusedon queueing theory and applications in communication.1" "Reasoning using desirability-based credal networks under epistemic irrelevance" "Gert De Cooman" "Department of Electromechanical, Systems and Metal Engineering" "Probabilistic graphical models describe complex problems in a manageable way they provide tools to answer questions and make decisions. Most such models force us to assess the uncertainties present precisely. We will present a mathematical description of a class of graphical models for situations where this is not possible. Algrorithms for constructing and using them will be proposed and applied." "FWO sabbatical bench fee professor De Cooman" "fdi  1) Lay the foundation for a monograph on imprecision in probability theory.2) Finalise current research on tree transformations, non-binary choice/preference models, and their connection with a propositionallogic of desirability statements.3) Initialise research on alternative characterisations of imprecise Schnorr randomness, and on algorithms for conservative inference inbinary and non-binary preference models."