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Matthias Troffaes

Professor, Probability

PhD Ghent University

AffiliationRoom numberTelephone
Professor, Probability in the Department of Mathematical SciencesMCS3035+44 (0) 191 33 43122


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.


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

  • decision making
  • foundations of probability and statistics
  • uncertainty modelling
  • risk
  • severe uncertainty
  • imprecise probability
  • engineering
  • renewable energy
  • environment

Research groups

  • Probability

Esteem Indicators

Media Contacts

Available for media contact about:

  • Statistics: I look at problems where too little information is available to apply traditional probabilistic methods successfully, and how we still can make decisions based on the really available information.


Authored book

  • Troffaes, Matthias C. M. & De Cooman, Gert (2014). Lower previsions. Wiley.

Chapter in book

Conference Paper

Conference Proceeding

  • Augustin, Thomas, Coolen, Frank P.A., Moral, Serafín & Troffaes, Matthias C. M. (2009). Proceedings of the Sixth International Symposium on Imprecise Probability: Theories and Applications. Sixth International Symposium on Imprecise Probability: Theories and Applications, Durham, UK, SIPTA.

Doctoral Thesis

  • Troffaes, Matthias C. M. (2005). Optimality, Uncertainty, and Dynamic Programming with Lower Previsions. Department of Electrical Energy, Systems & Automation. Universiteit Gent. PhD: 384.

Edited book

  • Augustin, Thomas, Coolen, Frank P. A., De Cooman, Gert & Troffaes, Matthias C. M. (2014). Introduction to Imprecise Probabilities. Wiley Series in Probability and Statistics. Wiley.
  • Coolen-Schrijner, Pauline, Coolen, Frank P. A., Troffaes, Matthias C. M., Augustin, Thomas & Gupta, Sat (2009). Imprecision in Statistical Theory and Practice. Grace Scientific Publishing.

Edited Journal

  • Augustin, Thomas, Coolen, Frank P. A., Moral, Serafin & Troffaes, Matthias C. M. (2010). International Journal of Approximate Reasoning. 51 (9): Elsevier.
  • Coolen, Frank P. A., Oberguggenberger, Michael & Troffaes, Matthias C. M. (2010). Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability. 224 (4).
  • Coolen-Schrijner, Pauline, Coolen, Frank, Troffaes, Matthias C. M. & Augustin, Thomas (2009). Journal of Statistical Theory and Practice. 3 (1): Grace Scientific Publishing.

Journal Article

Masters Thesis

  • Troffaes, Matthias C. M. (2000). Quantum algorithmes: theoretische aspecten en toepassingen. Universiteit Gent. Masters.

Other (Print)

  • Troffaes, Matthias C. M. (2004). Decision Making with Imprecise Probabilities: A Short Review. The SIPTA Newsletter 4-7.


Supervision students