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Professor Matthias Troffaes

Professor

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Professor in the Department of Mathematical Sciences

Biography

After receiving his MSc degree in engineering (theoretical physics) in 2000 from Gent University, Belgium, Matthias Troffaes joined the SYSTeMS research group at the same university as a doctoral researcher, pursuing research in imprecise probability theory under the guidance of Gert de Cooman, earning the degree of PhD in April 2005. In July 2005, he went to Carnegie Mellon University as a Francqui Foundation Fellow of the Belgian American Educational Foundation, working as a post-doctoral researcher with Teddy Seidenfeld. In September 2006, he joined the Department of Mathematical Sciences, Durham University, where he is currently Professor.

Research

My research is concerned with modelling and quantifying severe uncertainty and decision making under severe uncertainty. My interests lie in the theoretical probabilistic foundations behind such modelling, as well as practical statistical applications of such modelling.

In many practical applications, severe uncertainty arises due to insufficient data or expert opinion, relative to the complexity of the model. In such cases, it has been argued that no unique probability distribution can really honestly describe our knowledge. This discussion has a long history; see for instance Boole (1854), Keynes (1921), Williams (1975), Walley (1991), Weichselberger (1995), Shafer & Vovk (2001), Troffaes & De Cooman (2014), and many others.

For example, consider the probability that it rains on the day exactly twenty years from now. Experts may have a hard time to put a precise number on such probability, due to the complexity of climate modelling, but also due to uncertainty about climate change and about how politicians will respond it. However, experts may find it much easier to specify lower and upper bounds on such probability. From a Bayesian point of view, experts may have a hard time to put a precise prior distribution over such probability, but they may find it much easier to specify a set of prior distributions, for instance by bounding prior predictive quantities.

My work focuses on the mathematical theory for propagating probability bounds through models and through decision problems. I also look at practical statistical applications of such theories, mostly in engineering and in environmental sciences.

Research interests

  • probability bounding
  • mathematical statistics
  • foundations of probability and statistics
  • decision making
  • elicitation
  • risk
  • severe uncertainty
  • renewable energy
  • sustainability

Esteem Indicators

Publications

Authored book

Chapter in book

  • Foundations for temporal reasoning using lower previsions without a possibility space
    Troffaes, M. C., & Goldstein, M. (2022). Foundations for temporal reasoning using lower previsions without a possibility space. In T. Augustin, F. Gagliardi Cozman, & G. Wheeler (Eds.), Reflections on the Foundations of Probability and Statistics: Essays in Honor of Teddy Seidenfeld (69-96). (1). Springer Verlag. https://doi.org/10.1007/978-3-031-15436-2_4
  • Uncertainty Quantification in Lasso-Type Regularization Problems
    Basu, T., Einbeck, J., & Troffaes, M. C. (2021). Uncertainty Quantification in Lasso-Type Regularization Problems. In Optimization Under Uncertainty with Applications to Aerospace Engineering (81-109). Springer Verlag. https://doi.org/10.1007/978-3-030-60166-9_3
  • Decision making
    Huntley, N., Hable, R., & Troffaes, M. C. (2014). Decision making. In T. Augustin, F. P. Coolen, G. de Cooman, & M. C. Troffaes (Eds.), Introduction to Imprecise Probabilities (190-206). Wiley. https://doi.org/10.1002/9781118763117.ch8
  • Computation
    Troffaes, M. C., & Hable, R. (2014). Computation. In T. Augustin, F. P. Coolen, G. De Cooman, & M. C. Troffaes (Eds.), Introduction to Imprecise Probabilities (329-337). Wiley. https://doi.org/10.1002/9781118763117.ch16
  • Imprecise probability.
    Coolen, F. P., Troffaes, M. C., & Augustin, T. (2011). Imprecise probability. In M. Lovric (Ed.), International Encyclopedia of Statistical Science. Springer Verlag
  • Imprecision in Statistical Theory and Practice
    Coolen-Schrijner, P., Coolen, F. P., Troffaes, M. C., & Augustin, T. (2009). Imprecision in Statistical Theory and Practice. In P. Coolen-Schrijner, F. P. Coolen, M. C. Troffaes, & T. Augustin (Eds.), Imprecision in Statistical Theory and Practice. Grace Scientific Publishing
  • Efficient and Robust Global Amino Acid Sequence Alignment with Uncertain Evolutionary Distances
    Troffaes, M. C. (2006). Efficient and Robust Global Amino Acid Sequence Alignment with Uncertain Evolutionary Distances. In B. Bouchon-Meunier, G. Coletti, & R. Yager (Eds.), Modern Information Processing: From Theory to Applications (371-381). Elsevier
  • Extension of coherent lower previsions to unbounded random variables
    Troffaes, M. C., & De Cooman, G. (2003). Extension of coherent lower previsions to unbounded random variables. In B. Bouchon-Meunier, L. Foulloy, & R. Yager (Eds.), Intelligent Systems for Information Processing: From Representation to Applications (277-288). North-Holland. https://doi.org/10.1016/b978-044451379-3/50023-6

Conference Paper

Doctoral Thesis

Edited book

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Masters Thesis

Other (Print)

Presentation

Supervision students

Isha Saxena