Combinatorial Optimization
Stochastic Operations Research
Probability and Statistics
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Education
Research
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Probability and Statistics
Probability Theory is a mathematical discipline that plays an increasingly important role in our technological society. We are more and more often faced with organizations, systems and processes that are so complex that an explicit description is not feasible. Instead, probabilistic descriptions and methods of analyses are being used. Because of this, Probability Theory is internationally flourishing. We focus on probabilistic problems arising in physics (polymers, porous media and magnetization) and in telecommunication (wireless communication and coding techniques, and network modeling using random graphs).
In Statistics, the focus lies on modeling phenomena using statistical models to explain available data. In this technological age, we have large data sets at our disposal, for example in computational biology. The aim is to explain data using statistical models, thereby learning about the underlying processes that have produced these data sets. Specific areas of expertise include microarray analysis arising in gene analysis, monitoring procedures for industrial processes (control charts), design of experiments, statistical methods for software testing, and statistical signal processing techniques (nonparametric regression, wavelet analysis).
The Probability and Statistics Group is active in teaching. We teach courses for a wide range of audiences and educational programmes. Most courses that we teach are for our Bachelor's or Master's programme in applied and industrial mathematics, for other programmes at Eindhoven University of Technology, or for industrial teaching programmes.
Two general themes of research in the Probability and Statistics Group are the use of combinatorial techniques. In Statistics, a focus lies on computational issues, and the research in the group is quite applied. In probability, research has a strong statistical physics flavour. Applications in probability are mainly in electrical engineering (networking and telecommunications).
The group heavily
participates in EURANDOM,
both in the Random Spatial Structures and in the Statistical Information
and Modelling programs. The group also participates in LaQuSo.
All members of the group are in the
Stieltjes Research School.
A list of research topics, with the members of the group that perform research in these areas is given below:
- Non-parametric statistics (Alessandro Di Bucchianico, Laurie Davies)
- Statistical Process Control (Alessandro Di Bucchianico)
- Design of Experiments (Alessandro Di Bucchianico, Emiel van Berkum)
- Foundations of Statistics (Emiel van Berkum, Laurie Davies)
- Software Reliability (Alessandro Di Bucchianico)
- Large Deviations (Remco van der Hofstad)
- Non-Markovian stochastic processes such as Reinforced Random walks (Remco van der Hofstad)
- Combinatorial probability (Remco van der Hofstad)
- Random Graphs (Remco van der Hofstad)
- Stochastic Models for Telecommunication (Remco van der Hofstad)
- Probabilistic Polymer Models ( Remco van der Hofstad)
- Models for Porous Media ( Remco van der Hofstad)
- High-level image analysis ( Marie-Colette van Lieshout)
- Spatial statistics ( Marie-Colette van Lieshout)
- Point processes ( Marie-Colette van Lieshout)
- Random tessellations ( Marie-Colette van Lieshout)
- Stochastic geometry ( Marie-Colette van Lieshout)
In the past years, the group has performed several consultancy tasks, both with industry, as well as with other departments at the Eindhoven University of Technology. We also give some examples of internships in industry supervised by our group. A (non-exclusive) list of examples is given below.
Consultancy in Industry
We list a number of examples where members of our group were or are being involved in consultancy projects with industry. We also
list the areas of expertise involved:
- TNO (Statistical process control)
- Unilever (Design of experiments)
- Zeneca (Design of Experiments)
- Atos-Origin (Classical statistics)
- Ericsson (Software Reliability)
- Flextronics (Reliability, wavelets)
Consultancy at Eindhoven University of Technology
We list a number of examples where members of our group were involved in joint projects at Eindhoven University of Technology, and the leader of the group involved:
- Van Roermund (Electrical engineering, probabilistic modeling)
- Erik Fledderus (Electrical engineering, validity of Gaussian assumptions)
- Nico Adams (Chemistry, Design of Experiments)
- Kees van Hee and Jan Friso Groote (Software Reliability)
- Jan Fransoo (Regression analysis and Design of Experiments)
In these examples, we strive for joint publications in the application areas.
Internships in Industry
We list a number of examples where members of our group supervising students in internships in industry or at Eindhoven University of Technology. We also list the area of expertise that is being used:
- Douwe Egberts (Statistical Process Control)
- VTT Helsinki (Random Graphs)
For more information on consultancy in probability and statistics, please contact prof.dr. Remco van der Hofstad.
Graduationprojects
The P&S group offers the following graduationprojects:
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