Programme

On nonlinear semigroups and model uncertainty in finance
Prof Max Nendel
Universität Bielefeld, Center for Mathematical Economics (IMW)

In mathematical finance, model uncertainty or ambiguity is an almost omnipresent phenomenon, which, for example, appears, when certain aspects of an underlying asset cannot be determined precisely, or in the absence of sufficient data in order to perform reliable statistical estimation methods for the parameters of a stochastic process. The latter typically leads to so-called parameter uncertainty in the generator of the stochastic process. Under this type of uncertainty, worst case considerations together with dynamic consistency requirements lead to a stochastic optimal control problem, where, roughly speaking, “nature” tries to control the system into the worst possible scenario. In this talk, we illustrate how a class of optimal control problems arising in this context can be tackled using a semigroup-theoretic approach and give rise to imprecise versions of stochastic processes. We conclude by considering a second approach, where the uncertainty is captured in terms of a Wasserstein distance around a reference model.

Computing bounds for imprecise continuous-time Markov chains using normal cones
Prof Damjan Skulj, University of Ljubljana

The theory of imprecise Markov chains has achieved significant progress in recent years. Its applicability, however, is still very much limited, due in large part to the lack of efficient computational methods for calculating higher-dimensional models. The high computational complexity shows itself especially in the calculation of the imprecise version of the Kolmogorov backward equation. The equation is represented at every point of an interval in the form of a minimization problem, solvable merely with linear programming techniques. Consequently, finding an exact solution on an entire interval is infeasible, whence approximation approaches have been developed. To achieve sufficient accuracy, in general, the linear programming optimization methods need to be used in a large number of time points.

The principal goal of this talk is to provide a new, more efficient approach for solving the imprecise Kolmogorov backward equation. It is based on the Lipschitz continuity of the solutions of the equation with respect to time, causing the linear programming problems appearing in proximate points of the time interval having similar optimal solutions. This property is exploited by utilizing the theory of normal cones of convex sets. The present article is primarily devoted to providing the theoretical basis for the novel technique, yet, the initial testing shows that in most cases it decisively outperforms the existing methods.

11:30-12:00  Alexander Erreygers
Extending the domain of imprecise continuous-time Markov chains

12:00-12:30: Natan T’Joens
Characterising Game-Theoretic Upper Expectations in Discrete-Time Finite-State Stochastic Processes

12:30-13:00: Thomas Krak
Computing Expected Hitting Times for Imprecise Markov Chains

Imprecise probability for reliable and robust engineering analysis
Prof Edoardo Patelli, University of Strathclyde

The assessment of modern engineering systems and in particular for critical infrastructures is often performed with incomplete information, missing data and large unknowns. Strong initial assumptions may be needed to use classical probabilistic methods especially for cases affected by a lack of data. However, these assumptions can deeply influence the final results and lead to severe risk misjudgement by distorting the information regarding the true level of uncertainty affecting the system safety and giving a false sense of confidence. Furthermore, this classical implementation does not differentiate between different type of uncertainty. This is a severe limitation as it makes the analyst unable to grasp how much of the uncertainty is due to inherent variability and to what extent the uncertainty is due to poor data quality (therefore suitable to be reduced in principle).
Imprecise probability approaches have been introduced to better deal with scarce or limited information by adopting a more robust characterisation and propagation of different representation of the uncertainties (i.e. with less artificial assumptions for the characterisation of imprecise information). The use of generalised method to quantify uncertainty generally changes the representation of the output of interest from point-valued probabilistic estimators to non-crisp, imprecise (e.g. interval-valued or fuzzy) probabilistic estimators, truthfully representing the available (but incomplete) input data.
Although imprecise probability offers a more powerful representation of the uncertainty, applications of imprecise probability in engineering is still limited. This is often due to the lack of efficient computational tools and simulation techniques.
This talk will present an overview of efficient computation approaches for imprecise probability and their application for solving challenging engineering problems.

Imprecise inferences over Boolean functions made easy
Dr Sebastien Destercke, CNRS/UMR Heudiasyc

In this talk, we will briefly discuss the general problem of making inferences over Boolean functions when the truth values of variables are uncertainly known, and when this uncertainty is described by probability bounds. While such inferences are in general NP-hard to achieve, we will then focus on tractable subcases, illustrating their use in problems such as reliability analysis or short-term trajectory planning for autonomous vehicles (and moving robots in general). If times allow, we will then discuss open problems.

16:00-16:30: Cristian Greco
Robust Particle Filter for Space Navigation under Epistemic Uncertainty

16:30-17:00: Daniel Krpelik
Simultaneous Sampling for Robust Markov Chain Monte Carlo Inference

Imprecise Probability Approaches for the Statistical Modelling of Set-Valued Data
Prof Thomas Augustin, Department of Statistics, LMU Munich

The talk provides an overview of recent research on the statistical modelling of set-valued data. Set-valued data occur naturally in a variety of situations. In particular, they arise from inaccurate measurements, in the analysis of ranges, in the study of partially determined choices or from partial classification.

The choice of the statistical methods applicable is predetermined by two factors: the scale of measurement of the set-valued data and the interpretation of the set-valued character. There, Couso’s and Dubious’ distinction between epistemic imprecision (imprecise observation of something precise) and ontic imprecision (precise observation of something genuinely imprecise) is crucial.

For the continuous case, where set-valued data are typically interval-valued, we present an approach for generalized linear regression models that relies on set-valued solutions of likelihood-based score-functions. We sketch the relationship to some work in robust optimization and the area of partial identification, provide a formulation as a penalized optimization problem under linear constraints and discuss how to defy the curse of dimensionality by using ideas from statistical sufficiency.

For the categorical case, we provide a profile likelihood approach for multinomial regression models under epistemic imprecision, develop regularized choice models under ontic imprecision and finally discuss ideas for alternative modelling strategies and some extensions.

Wrap-up by symposium chairs:

• Prof Gert de Cooman (Ghent University, Belgium)
• Dr Jasper de Bock (Ghent University, Belgium)
• Prof Frank Coolen (Durham University, UK)

Dimensionality reduction and feature extraction from high-fidelity combustion data

Prof Alessandro Parente
Universite Libre de Bruxelles, Belgium

The use of machine learning algorithms to predict the behaviours of complex systems is booming. However, the key for an effective use of machine learning tools in multi-physics problems, including combustion, is to couple them to physical and computer models, to embody in them all the prior knowledge and physical constraints that can enhance their performances, and to improve them based on the feedback coming for the validation experiments. In other words, we need to adapt the scientific method to bring machine learning into the picture and make the best use of the massive amount of data we have produced thanks to the advances in numerical computing. 
The talk reviews some of the open opportunities for the application of data-driven, reduced-order modelling to combustion systems. In particular, the first webinar focuses on dimensionality reduction in the context of reacting flow applications. Different approaches (based on modal decomposition, neural networks, kernel methods) are presented and compared, based on their ability to identify low-dimensional manifold and provide relevant features.

Biography

Alessandro Parente got his Master Degree in Chemical Engineering at the Università di Pisa in 2005. He then carried out a PhD at the same University in collaboration with the University of Utah, where he served as Research Associate from November 2007 to December 2009. In April 2009, Prof Parente started working at the von Karman Institute of Fluid Dynamics. In October 2010, he was appointed Assistant Professor at the Aero-Thermo-Mechanical Department of Université Libre de Bruxelles. Since 2019, he is Professor at the same Institution. In January 2015, Prof Parente founded the BURN joint research group on combustion and robust optimization, involving 7 full time professors and around 40 researchers. His research interests are in the field of turbulent/chemistry interaction in turbulent combustion and reduced-order models, non-conventional fuels and pollutant formation in combustion systems, novel combustion technologies, numerical simulation of atmospheric boundary layer flows, and validation and uncertainty quantification. He is author and co-author of more than 75 papers on International Archival Journals.