# Staff

## Matthias Troffaes, PhD

**Director of Undergraduate Studies, Associate Professor (Reader), Statistics in the Department of Mathematical Sciences**

Contact Matthias Troffaes (email at matthias.troffaes@durham.ac.uk)

### Related Links

### Supervises

### Biography

After receiving his MSc degree in physical engineering 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 became a lecturer in statistics at the Department of Mathematical Sciences, Durham University.

### Research

My research is concerned with modelling severe uncertainty and decision making under severe uncertainty. My interests lie in the theoretical foundations behind such modelling, as well as practical 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 (Boole, 1854; Keynes, 1921; Williams, 1975; Walley, 1991; Shafer & Vovk, 2001; Troffaes & De Cooman, 2014).

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 Groups

- Statistics and Probability
- Statistics and Probability: Statistics
- Statistics and Probability: Statistics

### Research Interests

- Decision making
- Foundations of probability and statistics
- Uncertainty modelling
- Risk
- Severe uncertainty
- Imprecise probability
- Engineering
- Renewable energy
- Environment

### Teaching Areas

- Analytical Methods II (18 hours/year.)
- Bayesian Statistics III/IV (20 hours/year.)
- Decision Theory III (38 hours/year.)
- Operations Research III (20 hours/year.)
- Probability I (27 hours/year.)
- Statistics I (18 hours/year.)

### Selected Publications

#### Journal Article

- Edwards, Gruffudd,
**Sheehy, Sarah**, Dent, Chris &**Troffaes, Matthias C. M.**(Accepted). Assessing the Contribution of Grid-Scale Storage to Generation Capacity Adequacy.*Sustainable Energy, Grids and Networks* - Sahlin, Ullrika &
**Troffaes, Matthias C. M.**(2017). A note on EFSA’s ongoing efforts to increase transparency of uncertainty in scientific opinions.*Journal of Risk Research* - Miranda, Enrique,
**Troffaes, Matthias C. M.**& Destercke, Sébastien (2015). A geometric and game-theoretic study of the conjunction of possibility measures.*Information Sciences***298**: 373–389. - Greenwood, David M., Gentle, Jake P., Myers, Kurt S., Davison, Peter J., West, Isaac J., Bush, Jason W.,
**Ingram, Grant L.**&**Troffaes, Matthias C. M.**(2014). A Comparison of Real Time Thermal Rating Systems in the U.S. and the UK.*IEEE Transactions on Power Delivery***29**(4): 1849-1858. **Troffaes, Matthias C. M.**, Walter, Gero & Kelly, Dana (2014). A robust Bayesian approach to modelling epistemic uncertainty in common-cause failure models.*Reliability engineering & system safety***125**: 13-21.**Troffaes, Matthias C. M.**, Miranda, Enrique & Destercke, Sebastien (2013). On the connection between probability boxes and possibility measures.*Information Sciences***224**: 88-108.**Huntley, Nathan**&**Troffaes, Matthias C. M.**(2012). Normal Form Backward Induction for Decision Trees with Coherent Lower Previsions.*Annals of Operations Research***195**(1): 111-134.**Troffaes, Matthias C. M.**& Gosling, John Paul (2012). Robust detection of exotic infectious diseases in animal herds: A comparative study of three decision methodologies under severe uncertainty.*International Journal of Approximate Reasoning***53**(8): 1271-1281.**Troffaes, Matthias C. M.**& Destercke, Sébastien (2011). Probability boxes on totally preordered spaces for multivariate modelling.*International Journal of Approximate Reasoning***52**(6): 767-791.- Augustin, Thomas,
**Coolen, Frank P. A.**, Moral, Serafín &**Troffaes, Matthias C. M.**(2010). Imprecise probability in statistical inference and decision making.*International Journal of Approximate Reasoning***51**(9): 1011-1013. **Coolen, Frank P. A.**, Oberguggenberger, Michael &**Troffaes, Matthias C. M.**(2010). Uncertainty in Engineering Risk and Reliability: Introduction.*Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability***224**(4): i-vi.**Troffaes, Matthias**&**Coolen, Frank**(2009). Applying the imprecise Dirichlet model in cases with partial observations and dependencies in failure data.*International Journal of Approximate Reasoning***50**(2): 257-268.**Troffaes, Matthias**(2009). Finite approximations to coherent choice.*International Journal of Approximate Reasoning***50**(4): 655-665.- de Cooman, Gert,
**Troffaes, Matthias**& Miranda, Enrique (2008). A unifying approach to integration for bounded positive charges.*Journal of Mathematical Analysis and Applications***340**(2): 982-999. - de Cooman, Gert,
**Troffaes, Matthias**& Miranda, Enrique (2008). n-Monotone exact functionals.*Journal of Mathematical Analysis and Applications***347**(1): 143-156. **Troffaes, Matthias C.M.**(2007). Decision making under uncertainty using imprecise probabilities.*International Journal of Approximate Reasoning***45**(1): 17-29.**Troffaes, Matthias C. M.**(2006). Generalizing The Conjunction Rule for Aggregating Conflicting Expert Opinions.*International Journal of Intelligent Systems***21**(3): 361-380.- De Cooman, Gert &
**Troffaes, Matthias C. M.**(2005). Dynamic Programming for Deterministic Discrete-Time Systems with Uncertain Gain.*International Journal of Approximate Reasoning***39**(2-3): 257-278. - De Cooman, Gert,
**Troffaes, Matthias C. M.**& Miranda, Enrique (2005). n-Monotone lower previsions.*Journal of Intelligent & Fuzzy Systems***16**(4): 253-263. - De Cooman, Gert &
**Troffaes, Matthias C. M.**(2004). Coherent lower previsions in systems modelling: products and aggregation rules.*Reliability Engineering & System Safety***85**(1-3): 113-134.

#### Authored book

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

#### Chapter in book

**Troffaes, Matthias C. M.**& Hable, Robert (2014). Computation. In__Introduction to Imprecise Probabilities__. Augustin, Thomas,**Coolen, Frank P. A.**, De Cooman, Gert &**Troffaes, Matthias C. M.**Wiley. 329-337.**Huntley, Nathan**, Hable, Robert &**Troffaes, Matthias C. M.**(2014). Decision making. In__Introduction to Imprecise Probabilities__. Augustin, Thomas,**Coolen, Frank P. A.**, de Cooman, Gert &**Troffaes, Matthias C. M.**Wiley. 190-206.**Coolen, Frank P. A.**,**Troffaes, Matthias C. M.**& Augustin, Thomas (2011). Imprecise probability. In__International Encyclopedia of Statistical Science__. Lovric, Miodrag Springer.**Troffaes, Matthias C. M.**(2006). Efficient and Robust Global Amino Acid Sequence Alignment with Uncertain Evolutionary Distances. In__Modern Information Processing: From Theory to Applications__. Bouchon-Meunier, Bernadette, Coletti, Giulianella & Yager, Ronald Elsevier Science Ltd. 371-381.**Troffaes, Matthias C. M.**& De Cooman, Gert (2003). Extension of coherent lower previsions to unbounded random variables. In__Intelligent Systems for Information Processing: From Representation to Applications__. Bouchon-Meunier, B., Foulloy, L. & Yager, R. R. North-Holland. 277-288.

#### 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.

#### Conference Paper

**Troffaes, Matthias C. M.**(2017), A note on imprecise Monte Carlo over credal sets via importance sampling,__The Tenth International Symposium on Imprecise Probability: Theories and Applications (ISIPTA ’17)__. Lugano, Switzerland.**Nakharutai, Nawapon**,**Troffaes, Matthias C. M.**&**Caiado, Camila C. C. S.**(2017), Efficient algorithms for checking avoiding sure loss,__The Tenth International Symposium on Imprecise Probability: Theories and Applications (ISIPTA ’17)__. Lugano, Switzerland.**Troffaes, Matthias C. M.**& Sahlin, Ullrika (2017), Imprecise swing weighting for multi-attribute utility elicitation based on partial preferences,__The Tenth International Symposium on Imprecise Probability: Theories and Applications (ISIPTA ’17)__. Lugano, Switzerland.- Heylen, Evelyn,
**Troffaes, Matthias C. M.**,**Kazemtabrizi, Behzad**, Deconinck, Geert & Van Hertem, Dirk (2017), Qualitative comparison of techniques for evaluating performance of short term power system reliability management,__ISGT Europe 2017__. Torino, Italy. **Sheehy, S.**,**Edwards, G.**,**Dent, C. J.**,**Kazemtabrizi, B.**,**Troffaes, M. C. M.**& Tindemans, S. (2016), Impact of high wind penetration on variability of unserved energy in power system adequacy,__International Conference on Probabilistic Methods Applied to Power Systems (PMAPS)__. Beijing, IEEE, Piscataway, NJ, 1-6.**Paton, Lewis**,**Troffaes, Matthias C. M.**, Boatman, Nigel, Hussein, Mohamud & Hart, Andy (2015), A robust Bayesian analysis of the impact of policy decisions on crop rotations, in Augustin, T. , Doria, S. , Miranda, E. & Quaeghebeur, E. eds,__ISIPTA 2015__. Pescara, Italy, SIPTA, Pescara, 217-226.**Troffaes, Matthias C. M.**,**Williams, Edward**&**Dent, Chris J.**(2015), Data Analysis and Robust Modelling of the Impact of Renewable Generation on Long Term Security of Supply and Demand,__2015 IEEE Power & Energy Society General Meeting__. Denver, Colorado, US, IEEE, Piscataway, NJ, 1-5.**Troffaes, Matthias**,**Gledhill, Jacob**, Škulj, Damjan & Blake, Simon (2015), Using imprecise continuous time Markov chains for assessing the reliability of power networks with common cause failure and non-immediate repair, in Augustin, T. , Doria, S. , Miranda, E. & Quaeghebeur, E. eds,__ISIPTA 2015__. Pescara, Italy, Pescara, 287-294.**Troffaes, Matthias C. M.**,**Coolen, Frank P. A.**& Destercke, Sebastien (2014), A Note on Learning Dependence Under Severe Uncertainty, Communications in Computer and Information Science**444**:__Information Processing and Management of Uncertainty in Knowledge-Based Systems__. Montpellier, France, Springer, Montpellier, 498-507.**Paton, Lewis**,**Troffaes, Matthias C. M.**, Boatman, Nigel, Hussein, Mohamud & Hart, Andy (2014), Multinomial logistic regression on Markov chains for crop rotation modelling, Communications in Computer and Information Science**444**:__Information Processing and Management of Uncertainty in Knowledge-Based Systems__. Montpellier, France, Springer, Montpellier, 476-485.**Troffaes, Matthias C. M.**&**Goldstein, Michael**(2013), A Note on the Temporal Sure Preference Principle and the Updating of Lower Previsions, in Cozman, Fabio, Denoeux, Thierry, Destercke, Sebastien & Seidenfeld, Teddy eds,__ISIPTA'13: Proceedings of the Eighth International Symposium on Imprecise Probability: Theories and Applications__. Compiegne, France, SIPTA, Compiegne, 319-328.**Troffaes, Matthias C. M.**&**Blake, Simon**(2013), A Robust Data Driven Approach to Quantifying Common-Cause Failure in Power Networks, in Cozman, Fabio, Denoeux, Thierry, Destercke, Sebastien & Seidenfeld, Teddy eds,__ISIPTA'13: Proceedings of the Eighth International Symposium on Imprecise Probability: Theories and Applications__. Compiegne, France, SIPTA, Compiegne, 311-317.**Troffaes, Matthias C. M.**&**Paton, Lewis**(2013), Logistic Regression on Markov Chains for Crop Rotation Modelling, in Cozman, Fabio, Denoeux, Thierry, Destercke, Sebastien & Seidenfeld, Teddy eds,__ISIPTA'13: Proceedings of the Eighth International Symposium on Imprecise Probability: Theories and Applications__. Compiegne, France, SIPTA, Compiegne, 329-336.**Troffaes, Matthias C. M.**& Skulj, Damjan (2013), Model Checking for Imprecise Markov Chains, in Cozman, Fabio, Denoeux, Thierry, Destercke, Sebastien & Seidenfeld, Teddy eds,**Troffaes, Matthias C. M.**& Destercke, Sébastien (2012), A Nested Approach to Multivariate Modelling Using Lower Previsions,__11th International Probabilistic Safety Assessment and Management Conference and the Annual European Safety and Reliability Conference 2012 (PSAM11 ESREL 2012)__. Helsinki, Finland, Helsinki, 6764-6772.**Troffaes, Matthias C. M.**, Kelly, Dana L. &**Walter, Gero**(2012), Imprecise Dirichlet Model for Common-Cause Failure,__11th International Probabilistic Safety Assessment and Management Conference and the Annual European Safety and Reliability Conference 2012 (PSAM11 ESREL 2012)__. Helsinki, Finland, Helsinki, 6722-6728.**Huntley, Nathan**&**Troffaes, Matthias C. M.**(2011), Dynamic Programming and Subtree Perfectness for Deterministic Discrete-Time Systems with Uncertain Rewards, in**Coolen, Frank**, de Cooman, Gert, Fetz, Thomas & Oberguggenberger, Michael eds,__7th International Symposium on Imprecise Probability: Theories and Applications__. Innsbruck, SIPTA, Innsbruck, 209-218.**Troffaes, Matthias C. M.**, Kelly, Dana L. &**Walter, Gero**(2011), Elicitation and Inference for the Imprecise Dirichlet Model with Arbitrary Sets of Hyperparameters,__4th International Conference of the ERCIM (European Research Consortium for Informatics and Mathematics)__. 38-38.**Troffaes, Matthias C. M.**, Miranda, Enrique & Destercke, Sébastien (2011), On P-Boxes and Random Sets,__4th International Conference of the ERCIM (European Research Consortium for Informatics and Mathematics)__. 19-19.**Troffaes, Matthias C. M.**, Miranda, Enrique & Destercke, Sébastien (2011), On the connection between probability boxes and possibility measures,__7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT '11)__. Aix Les Bains, France, EUSFLAT, Aix Les Bains, 836-843.**Troffaes, Matthias C. M.**& Destercke, Sébastien (2011), Probability boxes on totally preordered spaces for multivariate modelling, in**Coolen, Frank**, de Cooman, Gert, Fetz, Thomas & Oberguggenberger, Michael eds,__7th International Symposium on Imprecise Probability: Theories and Applications__. Innsbruck, SIPTA, Innsbruck, 343-352.**Troffaes, Matthias C. M.**& Gosling, John Paul (2011), Robust detection of exotic infectious diseases in animal herds: A comparative study of two decision methodologies under severe uncertainty, in**Coolen, Frank**, de Cooman, Gert, Fetz, Thomas & Oberguggenberger, Michael eds,__7th International Symposium on Imprecise Probability: Theories and Applications__. Innsbruck, SIPTA, Innsbruck, 353-360.**Troffaes, Matthias C. M.**& Hable, Robert (2011), Robustness of Natural Extension, in**Coolen, Frank**, de Cooman, Gert, Fetz, Thomas & Oberguggenberger, Michael eds,__7th International Symposium on Imprecise Probability: Theories and Applications__. Innsbruck, SIPTA, Innsbruck, 361-370.**Troffaes, Matthias C. M.**, Huntley, Nathan & Shirota Filho, Ricardo (2010), Sequential Decision Processes under Act-State Independence with Arbitrary Choice Functions, in Hüllermeier, Eyke, Kruse, Rudolf & Hoffmann, Frank eds, Communications in Computer and Information Science**80**:__Information Processing and Management of Uncertainty in Knowledge-Based Systems__. Heidelberg, Springer, Heidelberg, 98-107.**Huntley, Nathan**&**Troffaes, Matthias**(2009), Characterizing factuality in normal form sequential decision making, in Augustin, Thomas,**Coolen, Frank**, Moral, Serafin &**Troffaes, Matthias**eds, ISIPTA'09: Proceedings of the Sixth International Symposium on Imprecise Probability: Theories and Applications__Sixth International Symposium on Imprecise Probability: Theories and Applications__. Durham, England, SIPTA, Durham, 239-248.**Huntley, Nathan**&**Troffaes, Matthias**(2008), An efficient normal form solution to decision trees with lower previsions, Advances in Soft Computing: Soft Methods for Handling Variability and Imprecision__Fourth International Workshop on Soft Methods in Probability and Statistics__. Toulouse, France, Springer, Toulouse, 419-426.- Miranda, Enrique,
**Troffaes, Matthias**& Destercke, Sebastien (2008), Generalised p-boxes on totally ordered spaces, Advances in Soft Computing: Soft Methods for Handling Variability and Imprecision__Fourth International Workshop on Soft Methods in Probability and Statistics__. Toulouse, France, Springer, Toulouse, 235-242. **Troffaes, Matthias C. M.**(2007), Finite approximations to coherent choice, in de Cooman, Gert de Cooman, Vejnarova, Jirina & Zaffalon, Marco eds, ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications__Fifth International Symposium on Imprecise Probability: Theories and Applications__. Prague, Czech Republic, Charles University, Faculty of Mathematics and Physics, Prague, 425-434.**Troffaes, Matthias C. M.**&**Coolen, Frank P. A.**(2007), On the use of the imprecise Dirichlet model in fault trees, Mathematical Methods in Reliability: Proceedings__Mathematical Methods in Reliability__. Glasgow, Scotland, University of Strathclyde, Glasgow.**Troffaes, Matthias C. M.**(2006), Conditional Lower Previsions for Unbounded Random Quantities, in Lawry, Jonathan, Miranda, Enrique, Bugarin, Alberto, Li, Shoumei, Ángeles Gil, Mariá, Grzegorzewski, Przemyslaw & Hryniewicz, Olgierd eds, Advances in Soft Computing: Soft Methods in Probability for Integrated Uncertainty Modelling__Third International Workshop on Soft Methods in Probability and Statistics__. Bristol, UK, Springer, Bristol, 201-209.- De Cooman, Gert,
**Troffaes, Matthias C. M.**& Miranda, Enrique (2005), n-Monotone lower previsions and lower integrals, in Cozman, Fabio G., Nau, Robert & Seidenfeld, Teddy eds,__Proceedings of the Fourth International Symposium on Imprecise Probabilities and Their Applications__. Pittsburgh, USA, Pittsburgh PA, 145-154. **Troffaes, Matthias C. M.**(2004), Adaptive control without prior by dynamic programming, in De Jager, Bram & Verdult, Vincent eds, 23rd Benelux Meeting on Systems and Control, Book of Abstracts__23rd Benelux Meeting on Systems and Control__. Eindhoven, Technische Universiteit Eindhoven, Eindhoven, 68-68.**Troffaes, Matthias C. M.**(2004), Efficient and Robust Global Amino Acid Sequence Alignment with Uncertain Evolutionary Distances, Proceedings of the Tenth International Conference IPMU 2004 (Information Processing and Management of Uncertainty in Knowledge-Based Systems)**1**:__Tenth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems__. Perugia, Italy, Perugia, 571-578.**Troffaes, Matthias C. M.**(2004), Learning and Optimal Control of Imprecise Markov Decision Processes by Dynamic Programming Using the Imprecise Dirichlet Model, in Lopéz-Díaz Miguel,, Gil, Maria A., Grzegorzewski, Przemyslaw, Hyrniewicz, Olgierd & Lawry, Jonathan eds, Soft Methodology and Random Information Systems__SMPS 2004__. Oviedo, Spain, Springer, Oviedo, 141-148.- De Cooman, Gert &
**Troffaes, Matthias C. M.**(2003), Dynamic Programming for Discrete-Time Systems with Uncertain Gain, in Bernard, Jean-Marc, Seidenfeld, Teddy & Zaffalon, Marco eds,__Proceedings of the Third International Symposium on Imprecise Probabilities and Their Applications (ISIPTA '03)__. Lugano, Switzerland, Carleton Scientific, Lugano, 162-176. **Troffaes, Matthias C. M.**(2003), Natural selection in aggregation or how evolutionary game theory may help in aggregating imprecise expert opinions,__7th workshop on dynamics and computation, iterated games and cooperation__. Heverlee, Belgium, Heverlee, 35-6.**Troffaes, Matthias C. M.**& De Cooman, Gert (2003), Reliable Interval Estimates for Download Times,__Fourth FTW PhD Symposium Faculty of Engineering, Ghent University__. Gent, Belgium, Ghent.**Troffaes, Matthias C. M.**(2003), Uncertainty and Conflict: A Behavioural Approach to the Aggregation of Expert Opinions, in Vejnarova, Jirina eds,__Proceedings of 6th Workshop on Uncertainty Processing (WUPES 2003)__. Hejnice, Czech Republic, VSE - Oeconomica Publishers, Hejnice, 263-277.**Troffaes, Matthias C. M.**& De Cooman, Gert (2002), Extension of Coherent Lower Previsions to Unbounded Random Variables,__Proceedings of the Ninth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU '02)__. Annecy, France, ESIA - Université de Savoie, Annecy, 735-42.**Troffaes, Matthias C. M.**& De Cooman, Gert (2002), Lower Previsions for Unbounded Random Variables, in Grzegorzewski, Przemyslaw, OHryniewicz, lgierd & Gil, Maria A. eds, Advances in Soft Computing__Soft Methods in Probability, Statistics and Data Analysis (SMPS '02)__. Warsaw, Poland, Physica-Verlag, Warsaw, 146-155.- De Cooman, Gert &
**Troffaes, Matthias C. M.**(2002), Optimal Control with Imprecise Gain through Dynamic Programming, in De Jager, Bram & Zwart, Hans eds, 21st Benelux Meeting on Systems and Control, Book of Abstracts__21st Benelux Meeting on Systems and Control__. Eindhoven, Technische Universiteit Eindhoven, Eindhoven, 94. **Troffaes, Matthias C. M.**& De Cooman, Gert (2002), The combination of conflicting information, Proceedings of the 3rd FTW PhD Symposium__3rd FTW PhD Symposium__. Gent, Belgium, Ghent.**Troffaes, Matthias C. M.**, De Cooman, Gert & Aeyels, Dirk (2001), Imprecise probabilities - discussion and open problems, Proceedings of the 2nd FTW PhD Symposium__2nd FTW PhD Symposium__. Gent, Belgium, Ghent.**Troffaes, Matthias C. M.**, De Cooman, Gert & Aeyels, Dirk (2001), Optimal control under imprecision, 20th Benelux Meeting on Systems and Control, Book of Abstracts__20th Benelux Meeting on Systems and Control__. 71-71.

#### 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 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.

#### 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.

#### Presentation

**Troffaes, Matthias C. M.**& Kelly, Dana (2011), Common-cause failure in wind turbines: an initial analysis, in**Coolen, Frank**, de Cooman, Gert, Fetz, Thomas & Oberguggenberger, Michael eds, Abstracts of Poster Only Presentations__7th International Symposium on Imprecise Probability: Theories and Applications__. Innsbruck, SIPTA, 33-33.