Staff profile

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.

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

• 2019: Secretary of SIPTA (Society for Imprecise Probability: Theories and Applications): I acted as secretary of the Society for Imprecise Probability: Theories and Applications (SIPTA). This society promotes research on imprecise probability through a series of activities. These activities bring together researchers from different groups, create resources for information, dissemination and documentation, and make other people aware of the potential of imprecise probability models.
• 2015: President of SIPTA (Society for Imprecise Probability: Theories and Applications): From July 2015 until June 2017, I have been president of the Society for Imprecise Probability: Theories and Applications (SIPTA).

Authored book

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

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 (1st ed., pp. 69-96). 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 (pp. 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 (pp. 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 (pp. 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 (pp. 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 (pp. 277-288). North-Holland. https://doi.org/10.1016/b978-044451379-3/50023-6

Conference Paper

• A robust Bayesian model to quantify and adjust for study quality and conflict of interest in meta-analyses
  
  Troffaes, M. C. M., Casini, L., Landes, J., & Sahlin, U. (in press). A robust Bayesian model to quantify and adjust for study quality and conflict of interest in meta-analyses. Proceedings of Machine Learning Research.
• Elicitation for decision problems under severe uncertainties
  
  Nakharutai, N., Troffaes, M., & Destercke, S. (2024). Elicitation for decision problems under severe uncertainties. In S. Destercke, M. Vanina Martinez, & G. Sanfilippo (Eds.), Scalable Uncertainty Management: 6th International Conference, SUM 2024 Palermo, Italy, November 27–29, 2024 Proceedings (pp. 312-324). https://doi.org/10.1007/978-3-031-76235-2_23
• Data-Driven Infrastructure Planning for Offshore Wind Farms
  
  Saxena, I., Kazemtabrizi, B., Troffaes, M. C., & Crabtree J., C. (2024). Data-Driven Infrastructure Planning for Offshore Wind Farms. Journal of Physics: Conference Series, 2767(6), Article 062002. https://doi.org/10.1088/1742-6596/2767/6/062002
• A Robust Bayesian Approach for Causal Inference Problems
  
  Basu, T., Troffaes, M. C. M., & Einbeck, J. (2023). A Robust Bayesian Approach for Causal Inference Problems. In Symbolic and Quantitative Approaches to Reasoning with Uncertainty (pp. 359-371). Springer Nature. https://doi.org/10.1007/978-3-031-45608-4_27
• A nonstandard approach to stochastic processes under probability bounding
  
  Troffaes, M. C. M. (2023). A nonstandard approach to stochastic processes under probability bounding. In E. Miranda, I. Montes, E. Quaeghebeur, & B. Vantaggi (Eds.), Proceedings of the Thirteenth International Symposium on Imprecise Probability: Theories and Applications (pp. 450-460). PMLR.
• Decision making under severe uncertainty on a budget
  
  Nakharutai, N., Destercke, S., & Troffaes, M. C. (2022). Decision making under severe uncertainty on a budget. In F. Dupin de Saint-Cyr, M. Öztürk-Escoffier, & N. Potyka (Eds.), Lecture Notes in Computer Science (pp. 186-201). Springer Verlag. https://doi.org/10.1007/978-3-031-18843-5_13
• Bayesian Adaptive Selection Under Prior Ignorance
  
  Basu, T., Troffaes, M. C., & Einbeck, J. (2021). Bayesian Adaptive Selection Under Prior Ignorance. In M. Vasile & D. Quagliarella (Eds.), Space Technology Proceedings (pp. 365-378). Springer Verlag. https://doi.org/10.1007/978-3-030-80542-5_22
• Binary Credal Classification Under Sparsity Constraints
  
  Basu, T., Troffaes, M. C., & Einbeck, J. (2020). Binary Credal Classification Under Sparsity Constraints. In M. Lesot, S. Vieira, M. Z. Reformat, J. P. Carvalho, A. Wilbik, B. Bouchon-Meunier, & R. R. Yager (Eds.), Information processing and management of uncertainty in knowledge-based systems : 18th International Conference, IPMU 2020, Lisbon, Portugal, June 15–19, 2020, proceedings, Part II. (pp. 82-95). Springer Verlag. https://doi.org/10.1007/978-3-030-50143-3_7
• A sensitivity analysis and error bounds for the adaptive lasso
  
  Basu, T., Einbeck, J., & Troffaes, M. (2020). A sensitivity analysis and error bounds for the adaptive lasso. In I. Irigoien, D. J. Lee, J. Martinez-Minaya, & M. X. Rodriguez-Alvarez (Eds.), Proceedings of the 35th International Workshop on Statistical Modelling. (pp. 278-281). Universidad del Pais Vasco.
• Robust uncertainty quantification for measurement problems with limited information
  
  Basu, T., Einbeck, J., Troffaes, M. C., & Forbes, A. (2019, July 3 – 2019, July 6). Robust uncertainty quantification for measurement problems with limited information [Conference paper]. Presented at ISIPTA 2019, Ghent, Belgium.
• Improving and benchmarking of algorithms for decision making with lower previsions
  
  Nakharutai, N., Troffaes, M. C., & Caiado, C. (2019, July 3 – 2019, July 6). Improving and benchmarking of algorithms for decision making with lower previsions [Conference paper]. Presented at ISIPTA 2019, Ghent, Belgium.
• Using interval dominance and Gamma-maximin for decision making in offshore power transmission
  
  Bains, H., Kazemtabrizi, B., Madariaga, A., & Troffaes, M. C. (2019, July 3 – 2019, July 6). Using interval dominance and Gamma-maximin for decision making in offshore power transmission [Conference paper]. Presented at ISIPTA 2019, Ghent, Belgium.
• The Impact of Offshore Transmission Regulatory Regimes on Technology Choices
  
  Bains, H., Madariaga, A., Kazemtabrizi, B., & Troffaes, M. C. (2019). The Impact of Offshore Transmission Regulatory Regimes on Technology Choices. In Proceedings of the Cigre Symposium Aalborg, 2019.. CIGRE.
• A Cantelli-type inequality for constructing non-parametric p-boxes based on exchangeability
  
  Troffaes, M. C., & Basu, T. (2019). A Cantelli-type inequality for constructing non-parametric p-boxes based on exchangeability. In J. D. Bock, C. P. . de Campos, G. de Cooman, E. Quaeghebeur, & G. Wheeler (Eds.), Proceedings of the Eleventh International Symposium on Imprecise Probabilities : Theories and Applications. (pp. 386-393). PMLR.
• A sensitivity analysis of adaptive lasso
  
  Basu, T., Einbeck, J., & Troffaes, M. C. (2019). A sensitivity analysis of adaptive lasso [Conference paper]. Presented at Innovations in Data and Statistical Sciences (INDSTATS 2019), Mumbai, India.
• Two-State Imprecise Markov Chains for Statistical Modelling of Two-State Non-Markovian Processes
  
  Troffaes, M. C., Krak, T., & Bains, H. (2019). Two-State Imprecise Markov Chains for Statistical Modelling of Two-State Non-Markovian Processes. In J. De Bock, C. P. de Campos, G. de Cooman, E. Quaeghebeur, & G. Wheeler (Eds.), Proceedings of the Eleventh International Symposium on Imprecise Probabilities : Theories and Applications. (pp. 394-403). PMLR.
• Contingency Ranking in Power Systems via Reliability Rates
  
  Cervantes, C., Kazemtabrizi, B., & Troffaes, M. (2018). Contingency Ranking in Power Systems via Reliability Rates. In 2018 IEEE International Conference on Environment and Electrical Engineering and 2018 IEEE Industrial and Commercial Power Systems Europe (EEEIC / I&CPS Europe) : 12-15 June, 2018, Palermo, Italy . Conference proceedings.. Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/eeeic.2018.8493853
• Iterative Importance Sampling for Estimating Expectation Bounds Under Partial Probability Specifications
  
  Troffaes, M. C., Fetz, T., & Oberguggenberger, M. (2018, July 16). Iterative Importance Sampling for Estimating Expectation Bounds Under Partial Probability Specifications. Presented at 8th International Workshop on Reliable Engineering Computing (REC2018), Liverpool, UK.
• Qualitative comparison of techniques for evaluating performance of short term power system reliability management
  
  Heylen, E., Deconinck, G., Van Hertem, D., Troffaes, M. C., & Kazemtabrizi, B. (2017). Qualitative comparison of techniques for evaluating performance of short term power system reliability management. In 2017 IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT-Europe) : Torino, Italy, 26-29 September 2017 : conference proceedings. (pp. 333-339). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/isgteurope.2017.8260148
• Imprecise swing weighting for multi-attribute utility elicitation based on partial preferences
  
  Troffaes, M. C., & Sahlin, U. (2017). Imprecise swing weighting for multi-attribute utility elicitation based on partial preferences. In A. Antonucci, G. Corani, I. Couso, & S. Destercke (Eds.), Proceedings of the Tenth International Symposium on Imprecise Probability : Theories and Applications, 10-14 July 2017, Lugano (Switzerland). (pp. 333-345). PMLR.
• Efficient algorithms for checking avoiding sure loss
  
  Nakharutai, N., Troffaes, M. C., & Caiado, C. C. (2017). Efficient algorithms for checking avoiding sure loss. In A. Antonucci, G. Corani, I. Couso, & S. Destercke (Eds.), Proceedings of the Tenth International Symposium on Imprecise Probability : Theories and Applications, 10-14 July 2017, Lugano (Switzerland). (pp. 241-252). PMLR.
• A note on imprecise Monte Carlo over credal sets via importance sampling
  
  Troffaes, M. C. (2017). A note on imprecise Monte Carlo over credal sets via importance sampling. In A. Antonucci, G. Corani, I. Couso, & S. Destercke (Eds.), Proceedings of the Tenth International Symposium on Imprecise Probability : Theories and Applications, 10-14 July 2017, Lugano (Switzerland). (pp. 325-332). PMLR.
• Impact of high wind penetration on variability of unserved energy in power system adequacy
  
  Sheehy, S., Edwards, G., Dent, C., Kazemtabrizi, B., Troffaes, M., & Tindemans, S. (2016). Impact of high wind penetration on variability of unserved energy in power system adequacy. In 2016 International Conference on Probabilistic Methods Applied to Power Systems (PMAPS) : Beijing, China, 16-20 October 2016 ; proceedings. (pp. 1-6). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/pmaps.2016.7764199
• Data Analysis and Robust Modelling of the Impact of Renewable Generation on Long Term Security of Supply and Demand
  
  Troffaes, M. C., Williams, E., & Dent, C. J. (2015). Data Analysis and Robust Modelling of the Impact of Renewable Generation on Long Term Security of Supply and Demand. In 2015 IEEE Power and Energy Society General Meeting. (pp. 1-5). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/pesgm.2015.7286070
• Using imprecise continuous time Markov chains for assessing the reliability of power networks with common cause failure and non-immediate repair
  
  Troffaes, M., Gledhill, J., Škulj, D., & Blake, S. (2015). Using imprecise continuous time Markov chains for assessing the reliability of power networks with common cause failure and non-immediate repair. In T. Augustin, S. Doria, E. Miranda, & E. Quaeghebeur (Eds.), ISIPTA ’15 : proceedings of the 9th International Symposium on Imprecise Probability : Theories and Applications, 20-24 July 2015, Pescara, Italy. (pp. 287-294). SIPTA.
• A robust Bayesian analysis of the impact of policy decisions on crop rotations
  
  Paton, L., Troffaes, M. C., Boatman, N., Hussein, M., & Hart, A. (2015). A robust Bayesian analysis of the impact of policy decisions on crop rotations. In T. Augustin, S. Doria, E. Miranda, & E. Quaeghebeur (Eds.), ISIPTA ’15 : proceedings of the 9th International Symposium on Imprecise Probability : Theories and Applications, 20-24 July 2015, Pescara, Italy. (pp. 217-226). SIPTA.
• A Note on Learning Dependence Under Severe Uncertainty
  
  Troffaes, M. C., Coolen, F. P., & Destercke, S. (2014). A Note on Learning Dependence Under Severe Uncertainty. In Information processing and management of uncertainty in knowledge-based systems : 15th International Conference, IPMU 2014, Montpellier, France, July 15-19, 2014 ; proceedings, part III. (pp. 498-507). Springer Verlag. https://doi.org/10.1007/978-3-319-08852-5_51
• Multinomial logistic regression on Markov chains for crop rotation modelling
  
  Paton, L., Troffaes, M. C., Boatman, N., Hussein, M., & Hart, A. (2014). Multinomial logistic regression on Markov chains for crop rotation modelling. In Information processing and management of uncertainty in knowledge-based systems : 15th International Conference, IPMU 2014, Montpellier, France, July 15-19, 2014 ; proceedings, part III. (pp. 476-485). Springer Verlag. https://doi.org/10.1007/978-3-319-08852-5_49
• A Note on the Temporal Sure Preference Principle and the Updating of Lower Previsions
  
  Troffaes, M. C., & Goldstein, M. (2013). A Note on the Temporal Sure Preference Principle and the Updating of Lower Previsions. In F. Cozman, T. Denoeux, S. Destercke, & T. Seidenfeld (Eds.), ISIPTA ’13 : proceedings of the eighth international symposium on imprecise probability : theories and applications July 2-5 2013, Compiègne, France. (pp. 319-328). Society for Imprecise Probability: Theories and Applications (SIPTA).
• Logistic Regression on Markov Chains for Crop Rotation Modelling
  
  Troffaes, M. C., & Paton, L. (2013). Logistic Regression on Markov Chains for Crop Rotation Modelling. In F. Cozman, T. Denoeux, S. Destercke, & T. Seidenfeld (Eds.), ISIPTA ’13 : proceedings of the eighth international symposium on imprecise probability : theories and applications July 2-5 2013, Compiègne, France. (pp. 329-336). Society for Imprecise Probability: Theories and Applications (SIPTA).
• Model Checking for Imprecise Markov Chains
  
  Troffaes, M. C., & Skulj, D. (2013). Model Checking for Imprecise Markov Chains. In F. Cozman, T. Denoeux, S. Destercke, & T. Seidenfeld (Eds.), ISIPTA ’13 : proceedings of the eighth international symposium on imprecise probability : theories and applications July 2-5 2013, Compiègne, France. (pp. 337-344). Society for Imprecise Probability: Theories and Applications (SIPTA).
• A Robust Data Driven Approach to Quantifying Common-Cause Failure in Power Networks
  
  Troffaes, M. C., & Blake, S. (2013). A Robust Data Driven Approach to Quantifying Common-Cause Failure in Power Networks. In F. Cozman, T. Denoeux, S. Destercke, & T. Seidenfeld (Eds.), ISIPTA ’13 : proceedings of the eighth international symposium on imprecise probability : theories and applications July 2-5 2013, Compiègne, France. (pp. 311-317). Society for Imprecise Probability: Theories and Applications (SIPTA).
• Imprecise Dirichlet Model for Common-Cause Failure
  
  Troffaes, M. C., Kelly, D. L., & Walter, G. (2012). Imprecise Dirichlet Model for Common-Cause Failure. Presented at 11th International Probabilistic Safety Assessment and Management Conference and the Annual European Safety and Reliability Conference 2012 (PSAM11 ESREL 2012), Helsinki, Finland.
• A Nested Approach to Multivariate Modelling Using Lower Previsions
  
  Troffaes, M. C., & Destercke, S. (2012). A Nested Approach to Multivariate Modelling Using Lower Previsions. Presented at 11th International Probabilistic Safety Assessment and Management Conference and the Annual European Safety and Reliability Conference 2012 (PSAM11 ESREL 2012), Helsinki, Finland.
• Probability boxes on totally preordered spaces for multivariate modelling
  
  Troffaes, M. C., & Destercke, S. (2011). Probability boxes on totally preordered spaces for multivariate modelling (F. Coolen, G. de Cooman, T. Fetz, & M. Oberguggenberger, Eds.). SIPTA.
• Dynamic Programming and Subtree Perfectness for Deterministic Discrete-Time Systems with Uncertain Rewards
  
  Huntley, N., & Troffaes, M. C. (2011). Dynamic Programming and Subtree Perfectness for Deterministic Discrete-Time Systems with Uncertain Rewards (F. Coolen, G. de Cooman, T. Fetz, & M. Oberguggenberger, Eds.). SIPTA.
• On P-Boxes and Random Sets
  
  Troffaes, M. C., Miranda, E., & Destercke, S. (2011). On P-Boxes and Random Sets. Presented at 4th International Conference of the ERCIM (European Research Consortium for Informatics and Mathematics).
• On the connection between probability boxes and possibility measures
  
  Troffaes, M. C., Miranda, E., & Destercke, S. (2011). On the connection between probability boxes and possibility measures. Presented at 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT ’11)., Aix Les Bains, France.
• Robust detection of exotic infectious diseases in animal herds: A comparative study of two decision methodologies under severe uncertainty
  
  Troffaes, M. C., & Gosling, J. P. (2011). Robust detection of exotic infectious diseases in animal herds: A comparative study of two decision methodologies under severe uncertainty (F. Coolen, G. de Cooman, T. Fetz, & M. Oberguggenberger, Eds.). SIPTA.
• Robustness of Natural Extension
  
  Troffaes, M. C., & Hable, R. (2011). Robustness of Natural Extension (F. Coolen, G. de Cooman, T. Fetz, & M. Oberguggenberger, Eds.). SIPTA.
• Elicitation and Inference for the Imprecise Dirichlet Model with Arbitrary Sets of Hyperparameters
  
  Troffaes, M. C., Kelly, D. L., & Walter, G. (2011). Elicitation and Inference for the Imprecise Dirichlet Model with Arbitrary Sets of Hyperparameters. Presented at 4th International Conference of the ERCIM (European Research Consortium for Informatics and Mathematics).
• Common-cause failure in wind turbines: an initial analysis
  
  Troffaes, M. C., & Kelly, D. (2011). Common-cause failure in wind turbines: an initial analysis [Conference paper] (F. Coolen, G. de Cooman, T. Fetz, & M. Oberguggenberger, Eds.). Presented at 7th International Symposium on Imprecise Probability: Theories and Applications, Innsbruck.
• Sequential Decision Processes under Act-State Independence with Arbitrary Choice Functions
  
  Troffaes, M. C., Huntley, N., & Shirota Filho, R. (2010). Sequential Decision Processes under Act-State Independence with Arbitrary Choice Functions. In E. Hüllermeier, R. Kruse, & F. Hoffmann (Eds.), Communications in Computer and Information Science (pp. 98-107). Springer Verlag.
• Characterizing factuality in normal form sequential decision making.
  
  Huntley, N., & Troffaes, M. (2009). Characterizing factuality in normal form sequential decision making. In T. Augustin, F. Coolen, S. Moral, & M. Troffaes (Eds.), ISIPTA’09: Proceedings of the Sixth International Symposium on Imprecise Probability: Theories and Applications..
• Proceedings of the Sixth International Symposium on Imprecise Probability: Theories and Applications
  
  Augustin, T., Coolen, F. P., Moral, S., & Troffaes, M. C. M. (Eds.). (2009, July). Proceedings of the Sixth International Symposium on Imprecise Probability: Theories and Applications. Presented at Sixth International Symposium on Imprecise Probability: Theories and Applications., Durham, UK.
• Generalised p-boxes on totally ordered spaces.
  
  Miranda, E., Troffaes, M., & Destercke, S. (2008). Generalised p-boxes on totally ordered spaces. In Advances in Soft Computing: Soft Methods for Handling Variability and Imprecision (pp. 235-242). Springer Verlag.
• An efficient normal form solution to decision trees with lower previsions.
  
  Huntley, N., & Troffaes, M. (2008). An efficient normal form solution to decision trees with lower previsions. In Advances in Soft Computing: Soft Methods for Handling Variability and Imprecision (pp. 419-426). Springer Verlag.
• On the use of the imprecise Dirichlet model in fault trees.
  
  Troffaes, M. C., & Coolen, F. P. (2007). On the use of the imprecise Dirichlet model in fault trees. In Mathematical Methods in Reliability: Proceedings. University of Strathclyde.
• Finite approximations to coherent choice.
  
  Troffaes, M. C. (2007). Finite approximations to coherent choice. In G. de C. de Cooman, J. Vejnarova, & M. Zaffalon (Eds.), ISIPTA’07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications (pp. 425-434). Charles University, Faculty of Mathematics and Physics.
• Conditional Lower Previsions for Unbounded Random Quantities
  
  Troffaes, M. C. (2006). Conditional Lower Previsions for Unbounded Random Quantities. In J. Lawry, E. Miranda, A. Bugarin, S. Li, M. Ángeles Gil, P. Grzegorzewski, & O. Hryniewicz (Eds.), Advances in Soft Computing: Soft Methods in Probability for Integrated Uncertainty Modelling. (pp. 201-209). Springer Verlag.
• n-Monotone lower previsions and lower integrals
  
  De Cooman, G., Troffaes, M. C., & Miranda, E. (2005). n-Monotone lower previsions and lower integrals (F. G. Cozman, R. Nau, & T. Seidenfeld, Eds.).
• Efficient and Robust Global Amino Acid Sequence Alignment with Uncertain Evolutionary Distances
  
  Troffaes, M. C. (2004). Efficient and Robust Global Amino Acid Sequence Alignment with Uncertain Evolutionary Distances. In Proceedings of the Tenth International Conference IPMU 2004 (Information Processing and Management of Uncertainty in Knowledge-Based Systems) (pp. 571-578).
• Adaptive control without prior by dynamic programming
  
  Troffaes, M. C. (2004). Adaptive control without prior by dynamic programming. In B. De Jager & V. Verdult (Eds.), 23rd Benelux Meeting on Systems and Control, Book of Abstracts (pp. 68-68). Technische Universiteit Eindhoven.
• Learning and Optimal Control of Imprecise Markov Decision Processes by Dynamic Programming Using the Imprecise Dirichlet Model
  
  Troffaes, M. C. (2004). Learning and Optimal Control of Imprecise Markov Decision Processes by Dynamic Programming Using the Imprecise Dirichlet Model. In L. Miguel, M. A. Gil, P. Grzegorzewski, O. Hyrniewicz, & J. Lawry (Eds.), Soft Methodology and Random Information Systems (pp. 141-148). Springer Verlag.
• Reliable Interval Estimates for Download Times
  
  Troffaes, M. C., & De Cooman, G. (2003, December). Reliable Interval Estimates for Download Times. Presented at Fourth FTW PhD Symposium Faculty of Engineering, Ghent University, Gent, Belgium.
• Natural selection in aggregation or how evolutionary game theory may help in aggregating imprecise expert opinions
  
  Troffaes, M. C. (2003, October). Natural selection in aggregation or how evolutionary game theory may help in aggregating imprecise expert opinions. Presented at 7th workshop on dynamics and computation, iterated games and cooperation, Heverlee, Belgium.
• Uncertainty and Conflict: A Behavioural Approach to the Aggregation of Expert Opinions
  
  Troffaes, M. C. (2003). Uncertainty and Conflict: A Behavioural Approach to the Aggregation of Expert Opinions (J. Vejnarova, Ed.). VSE - Oeconomica Publishers.
• Dynamic Programming for Discrete-Time Systems with Uncertain Gain
  
  De Cooman, G., & Troffaes, M. C. (2003). Dynamic Programming for Discrete-Time Systems with Uncertain Gain (J. Bernard, T. Seidenfeld, & M. Zaffalon, Eds.). Carleton Scientific.
• The combination of conflicting information
  
  Troffaes, M. C., & De Cooman, G. (2002). The combination of conflicting information. In Proceedings of the 3rd FTW PhD Symposium.
• Lower Previsions for Unbounded Random Variables
  
  Troffaes, M. C., & De Cooman, G. (2002). Lower Previsions for Unbounded Random Variables. In P. Grzegorzewski, lgierd OHryniewicz, & M. A. Gil (Eds.), Advances in Soft Computing (pp. 146-155). Physica Verlag.
• Extension of Coherent Lower Previsions to Unbounded Random Variables
  
  Troffaes, M. C., & De Cooman, G. (2002, July). Extension of Coherent Lower Previsions to Unbounded Random Variables. Presented at Proceedings of the Ninth International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU ’02), Annecy, France.
• Optimal Control with Imprecise Gain through Dynamic Programming
  
  De Cooman, G., & Troffaes, M. C. (2002). Optimal Control with Imprecise Gain through Dynamic Programming. In B. De Jager & H. Zwart (Eds.), 21st Benelux Meeting on Systems and Control, Book of Abstracts. Technische Universiteit Eindhoven.
• Imprecise probabilities - discussion and open problems
  
  Troffaes, M. C., De Cooman, G., & Aeyels, D. (2001). Imprecise probabilities - discussion and open problems. In Proceedings of the 2nd FTW PhD Symposium.
• Optimal control under imprecision
  
  Troffaes, M. C., De Cooman, G., & Aeyels, D. (2001). Optimal control under imprecision. In 20th Benelux Meeting on Systems and Control, Book of Abstracts (pp. 71-71).

Doctoral Thesis

• Optimality, Uncertainty, and Dynamic Programming with Lower Previsions
  
  Troffaes, M. C. (2005). Optimality, Uncertainty, and Dynamic Programming with Lower Previsions [Thesis]. Department of Electrical Energy, Systems & Automation, Universiteit Gent.

Edited book

• Introduction to Imprecise Probabilities
  
  Augustin, T., Coolen, F. P., De Cooman, G., & Troffaes, M. C. (Eds.). (2014). Introduction to Imprecise Probabilities. Wiley.
• Imprecision in Statistical Theory and Practice
  
  Coolen-Schrijner, P., Coolen, F. P., Troffaes, M. C., Augustin, T., & Gupta, S. (Eds.). (2009). Imprecision in Statistical Theory and Practice. Grace Scientific Publishing.

Journal Article

• Robust Bayesian causal estimation for causal inference in medical diagnosis
  
  Basu, T., & Troffaes, M. C. M. (2025). Robust Bayesian causal estimation for causal inference in medical diagnosis. International Journal of Approximate Reasoning, 177, Article 109330. https://doi.org/10.1016/j.ijar.2024.109330
• Data-driven estimation of the amount of under frequency load shedding in small power systems
  
  Rajabdorri, M., Troffaes, M. C. M., Kazemtabrizi, B., Sarvarizadeh, M., Sigrist, L., & Lobato, E. (2025). Data-driven estimation of the amount of under frequency load shedding in small power systems. Engineering Applications of Artificial Intelligence, 139(Part B), Article 109617. https://doi.org/10.1016/j.engappai.2024.109617
• Regret-based budgeted decision rules under severe uncertainty
  
  Nakharutai, N., Destercke, S., & Troffaes, M. C. M. (2024). Regret-based budgeted decision rules under severe uncertainty. Information Sciences, 665, Article 120361. https://doi.org/10.1016/j.ins.2024.120361
• Inclusion of frequency nadir constraint in the unit commitment problem of small power systems using machine learning
  
  Rajabdorri, M., Kazemtabrizi, B., Troffaes, M., Sigrist, L., & Lubato, E. (2023). Inclusion of frequency nadir constraint in the unit commitment problem of small power systems using machine learning. Sustainable Energy, Grids and Networks, 36, Article 101161. https://doi.org/10.1016/j.segan.2023.101161
• A robust Bayesian analysis of variable selection under prior ignorance
  
  Basu, T., Troffaes, M. C., & Einbeck, J. (2023). A robust Bayesian analysis of variable selection under prior ignorance. Sankhya A, 85(1), 1014-1057. https://doi.org/10.1007/s13171-022-00287-2
• Iterative importance sampling with Markov chain Monte Carlo sampling in robust Bayesian analysis
  
  Raices Cruz, I., Lindström, J., Troffaes, M. C., & Sahlin, U. (2022). Iterative importance sampling with Markov chain Monte Carlo sampling in robust Bayesian analysis. Computational Statistics & Data Analysis, 176, Article 107558. https://doi.org/10.1016/j.csda.2022.107558
• A robust Bayesian bias-adjusted random effects model for consideration of uncertainty about bias terms in evidence synthesis
  
  Raices Cruz, I., Troffaes, M. C., Lindström, J., & Sahlin, U. (2022). A robust Bayesian bias-adjusted random effects model for consideration of uncertainty about bias terms in evidence synthesis. Statistics in Medicine, 41(17), 3365-3379. https://doi.org/10.1002/sim.9422
• A suggestion for the quantification of precise and bounded probability to quantify epistemic uncertainty in scientific assessments
  
  Raices Cruz, I., Troffaes, M., & Sahlin, U. (2022). A suggestion for the quantification of precise and bounded probability to quantify epistemic uncertainty in scientific assessments. Risk Analysis, 42(2), 239-253. https://doi.org/10.1111/risa.13871
• Inclusion of Frequency Stability Constraints in Unit Commitment Using Separable Programming
  
  Ferrandon-Cervantes, C., Kazemtabrizi, B., & Troffaes, M. (2022). Inclusion of Frequency Stability Constraints in Unit Commitment Using Separable Programming. Electric Power Systems Research, 203, Article 107669. https://doi.org/10.1016/j.epsr.2021.107669
• Robust decision analysis under severe uncertainty and ambiguous tradeoffs: an invasive species case study
  
  Sahlin, U., Troffaes, M. C., & Edsman, L. (2021). Robust decision analysis under severe uncertainty and ambiguous tradeoffs: an invasive species case study. Risk Analysis, 41(11), 2140-2153. https://doi.org/10.1111/risa.13722
• Improving and benchmarking of algorithms for Γ-maximin, Γ-maximax and interval dominance
  
  Nakharutai, N., Troffaes, M. C., & Caiado, C. C. (2021). Improving and benchmarking of algorithms for Γ-maximin, Γ-maximax and interval dominance. International Journal of Approximate Reasoning, 133, 95-115. https://doi.org/10.1016/j.ijar.2021.03.005
• Modelling of modular battery systems under cell capacity variation and degradation
  
  Rogers, D. J., Aslett, L. J., & Troffaes, M. C. (2021). Modelling of modular battery systems under cell capacity variation and degradation. Applied Energy, 43, Article 116360. https://doi.org/10.1016/j.apenergy.2020.116360
• A note on EFSA’s ongoing efforts to increase transparency of uncertainty in scientific opinions
  
  Sahlin, U., & Troffaes, M. C. (2021). A note on EFSA’s ongoing efforts to increase transparency of uncertainty in scientific opinions. Journal of Risk Research, 24(5), 545-552. https://doi.org/10.1080/13669877.2017.1313769
• An Economic Model for Offshore Transmission Asset Planning Under Severe Uncertainty
  
  Bains, H., Madariaga, A., Troffaes, M. C., & Kazemtabrizi, B. (2020). An Economic Model for Offshore Transmission Asset Planning Under Severe Uncertainty. Renewable Energy, 160, 1174-1184. https://doi.org/10.1016/j.renene.2020.05.160
• A review of methods to study resilience of complex engineering and engineered systems
  
  Naghshbandi, S. N., Varga, L., Purvis, A., Mcwilliam, R., Minisci, E., Vasile, M., Troffaes, M., Sedighi, T., Guo, W., Manley, E., & Jones, D. H. (2020). A review of methods to study resilience of complex engineering and engineered systems. IEEE Access, 8(1), 87775-87799. https://doi.org/10.1109/access.2020.2992239
• Improving and benchmarking of algorithms for decision making with lower previsions
  
  Nakharutai, N., Troffaes, M. C., & Caiado, C. (2019). Improving and benchmarking of algorithms for decision making with lower previsions. International Journal of Approximate Reasoning, 113, 91-105. https://doi.org/10.1016/j.ijar.2019.06.008
• Evaluating betting odds and free coupons using desirability
  
  Nakharutai, N., Caiado, C. C., & Troffaes, M. C. (2019). Evaluating betting odds and free coupons using desirability. International Journal of Approximate Reasoning, 106, 128-145. https://doi.org/10.1016/j.ijar.2019.01.002
• Improved linear programming methods for checking avoiding sure loss
  
  Nakharutai, N., Troffaes, M. C., & Caiado, C. C. (2018). Improved linear programming methods for checking avoiding sure loss. International Journal of Approximate Reasoning, 101, 293-310. https://doi.org/10.1016/j.ijar.2018.07.013
• Imprecise Monte Carlo simulation and iterative importance sampling for the estimation of lower previsions
  
  Troffaes, M. C. (2018). Imprecise Monte Carlo simulation and iterative importance sampling for the estimation of lower previsions. International Journal of Approximate Reasoning, 101, 31-48. https://doi.org/10.1016/j.ijar.2018.06.009
• Assessing the Contribution of Nightly Rechargeable Grid-Scale Storage to Generation Capacity Adequacy
  
  Edwards, G., Sheehy, S., Dent, C., & Troffaes, M. C. (2017). Assessing the Contribution of Nightly Rechargeable Grid-Scale Storage to Generation Capacity Adequacy. Sustainable Energy, Grids and Networks, 12, 69-81. https://doi.org/10.1016/j.segan.2017.09.005
• A geometric and game-theoretic study of the conjunction of possibility measures
  
  Miranda, E., Troffaes, M. C., & Destercke, S. (2015). A geometric and game-theoretic study of the conjunction of possibility measures. Information Sciences, 298, 373-389. https://doi.org/10.1016/j.ins.2014.10.067
• A Comparison of Real Time Thermal Rating Systems in the U.S. and the UK
  
  Greenwood, D. M., Gentle, J. P., Myers, K. S., Davison, P. J., West, I. J., Bush, J. W., Ingram, G. L., & Troffaes, M. C. (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. https://doi.org/10.1109/tpwrd.2014.2299068
• A robust Bayesian approach to modelling epistemic uncertainty in common-cause failure models
  
  Troffaes, M. C., Walter, G., & Kelly, D. (2014). A robust Bayesian approach to modelling epistemic uncertainty in common-cause failure models. Reliability Engineering and System Safety, 125, 13-21. https://doi.org/10.1016/j.ress.2013.05.022
• On the connection between probability boxes and possibility measures
  
  Troffaes, M. C., Miranda, E., & Destercke, S. (2013). On the connection between probability boxes and possibility measures. Information Sciences, 224, 88-108. https://doi.org/10.1016/j.ins.2012.09.033
• Robust detection of exotic infectious diseases in animal herds: A comparative study of three decision methodologies under severe uncertainty
  
  Troffaes, M. C., & Gosling, J. P. (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. https://doi.org/10.1016/j.ijar.2012.06.020
• Normal Form Backward Induction for Decision Trees with Coherent Lower Previsions
  
  Huntley, N., & Troffaes, M. C. (2012). Normal Form Backward Induction for Decision Trees with Coherent Lower Previsions. Annals of Operations Research, 195(1), 111-134. https://doi.org/10.1007/s10479-011-0968-2
• Probability boxes on totally preordered spaces for multivariate modelling
  
  Troffaes, M. C., & Destercke, S. (2011). Probability boxes on totally preordered spaces for multivariate modelling. International Journal of Approximate Reasoning, 52(6), 767-791. https://doi.org/10.1016/j.ijar.2011.02.001
• Imprecise probability in statistical inference and decision making
  
  Augustin, T., Coolen, F. P., Moral, S., & Troffaes, M. C. (2010). Imprecise probability in statistical inference and decision making. International Journal of Approximate Reasoning, 51(9), 1011-1013. https://doi.org/10.1016/j.ijar.2010.08.001
• Uncertainty in Engineering Risk and Reliability: Introduction
  
  Coolen, F. P., Oberguggenberger, M., & Troffaes, M. C. (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.
• Finite approximations to coherent choice
  
  Troffaes, M. (2009). Finite approximations to coherent choice. International Journal of Approximate Reasoning, 50(4), 655-665. https://doi.org/10.1016/j.ijar.2008.07.001
• Imprecision in Statistical Theory and Practice
  
  Coolen-Schrijner, P., Coolen, F. P., Troffaes, M. C., & Augustin, T. (2009). Imprecision in Statistical Theory and Practice. Journal of Statistical Theory and Practice, 3(1), 1-9.
• Applying the imprecise Dirichlet model in cases with partial observations and dependencies in failure data
  
  Troffaes, M., & Coolen, F. (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. https://doi.org/10.1016/j.ijar.2008.03.013
• n-Monotone exact functionals
  
  de Cooman, G., Troffaes, M., & Miranda, E. (2008). n-Monotone exact functionals. Journal of Mathematical Analysis and Applications, 347(1), 143-156. https://doi.org/10.1016/j.jmaa.2008.05.071
• A unifying approach to integration for bounded positive charges
  
  de Cooman, G., Troffaes, M., & Miranda, E. (2008). A unifying approach to integration for bounded positive charges. Journal of Mathematical Analysis and Applications, 340(2), 982-999. https://doi.org/10.1016/j.jmaa.2007.09.026
• Decision making under uncertainty using imprecise probabilities
  
  Troffaes, M. C. (2007). Decision making under uncertainty using imprecise probabilities. International Journal of Approximate Reasoning, 45(1), 17-29. https://doi.org/10.1016/j.ijar.2006.06.001
• Generalizing The Conjunction Rule for Aggregating Conflicting Expert Opinions
  
  Troffaes, M. C. (2006). Generalizing The Conjunction Rule for Aggregating Conflicting Expert Opinions. International Journal of Intelligent Systems, 21(3), 361-380. https://doi.org/10.1002/int.20140
• n-Monotone lower previsions
  
  De Cooman, G., Troffaes, M. C., & Miranda, E. (2005). n-Monotone lower previsions. Journal of Intelligent and Fuzzy Systems, 16(4), 253-263.
• Dynamic Programming for Deterministic Discrete-Time Systems with Uncertain Gain
  
  De Cooman, G., & Troffaes, M. C. (2005). Dynamic Programming for Deterministic Discrete-Time Systems with Uncertain Gain. International Journal of Approximate Reasoning, 39(2-3), 257-278. https://doi.org/10.1016/j.ijar.2004.10.004
• Coherent lower previsions in systems modelling: products and aggregation rules
  
  De Cooman, G., & Troffaes, M. C. (2004). Coherent lower previsions in systems modelling: products and aggregation rules. Reliability Engineering and System Safety, 85(1-3), 113-134. https://doi.org/10.1016/j.ress.2004.03.007

Masters Thesis

• Quantum algorithmes: theoretische aspecten en toepassingen
  
  Troffaes, M. C. (2000). Quantum algorithmes: theoretische aspecten en toepassingen [Dissertation]. Universiteit Gent.

Other (Print)

• Decision Making with Imprecise Probabilities: A Short Review
  
  Troffaes, M. C. (2004). Decision Making with Imprecise Probabilities: A Short Review (F. G. Cozman, Ed.; pp. 4-7). The SIPTA Newsletter.

Presentation

• Sensitivity analysis of Bayesian variable selection and its application in causal estimation
  
  Basu, T., Einbeck, J., & Troffaes, M. C. M. (2025, July 15 – 2025, July 18). Sensitivity analysis of Bayesian variable selection and its application in causal estimation [Poster]. Presented at 14th International Symposium on Imprecise Probabilities: Theories and Applications, Bielefeld, Germany.
• Using probability bounding to improve decision making for offshore wind planning in industry
  
  Troffaes, M. C. M., Kazemtabrizi, B., Smallbone, A., Bains, H., Jenkins, A., & McKeever, P. (2023, July 11 – 2023, July 14). Using probability bounding to improve decision making for offshore wind planning in industry [Poster]. Presented at 13th International Symposium on Imprecise Probability: Theories and Applications, Oviedo, Spain.
• A constructive theory for conditional lower previsions only using rational valued probability mass functions with finite support
  
  Troffaes, M. C. M. (2023, July 11 – 2023, July 14). A constructive theory for conditional lower previsions only using rational valued probability mass functions with finite support [Poster]. Presented at 13th International Symposium on Imprecise Probability: Theories and Applications, Oviedo, Spain.