Diffusion processes are natural statistical models for many phenomena, such as modelling financial time series and dynamics of biological systems. In practice, available data are obtained discretely in time and usually incomplete, in the sense that some function of the state of the diffusion is observed. The statistical analysis of such data poses a formidable problem. Over the past decades there has been much research on this problem and progress has been made in developing Bayesian computational methods, mainly using Markov Chain Monte Carlo (MCMC) methods. Unfortunately, these methods are computationally demanding and in their present form only allow for estimation in diffusion models of low dimension. Many applications however utilise models of high dimension.

It is the aim of this project to develop computational methods for estimating diffusions in high dimension. Over the past decade, various novel Monte Carlo techniques have been developed to deal with ``big data'' settings. These methods are typically developed for statistical models where the observations are treated as independent and identically distributed. A recent breakthrough in MCMC is the Zig-Zag sampler which for the first time allows to use sub-sampling to reduce a Monte Carlo simulation problem into smaller components. It is the aim of this PhD project to apply the Zig-Zag algorithm to inference of diffusion processes. This poses several interesting challenges.

The student will be supervised by Dr.ir. J. Bierkens (TU Delft) and Dr.ir. F.H. van der Meulen (TU Delft) within the group lead by Prof.dr.ir. G. Jongbloed. The position includes modest teaching duties. The candidate is expected to finish his/her project with a PhD thesis, and disseminate the results through publications in peer-reviewed journals, and presentations at international conferences. 

The candidate possesses an MSc degree in mathematics (specialisation statistics or probability theory) or a related discipline such as physics, computer science or econometrics (with strong emphasis on mathematics, statistics and/or machine learning). (S)he must be highly motivated and ambitious with a strong curriculum in statistics and stochastic processes. As this project falls within computational statistics and stochastic simulation, good programming skills are highly relevant. In addition, we require very good communication skills and fluently spoken and written English.

Fixed-term contract: 4 years.

TU Delft offers a customisable compensation package, a discount for health insurance and sport memberships, and a monthly work costs contribution. Flexible work schedules can be arranged. An International Children’s Centre offers childcare and an international primary school. Dual Career Services offers support to accompanying partners. Salary and benefits are in accordance with the Collective Labour Agreement for Dutch Universities.

As a PhD candidate you will be enrolled in the TU Delft Graduate School. TU Delft Graduate School provides an inspiring research environment; an excellent team of supervisors, academic staff and a mentor; and a Doctoral Education Programme aimed at developing your transferable, discipline-related and research skills. Please visit www.tudelft.nl/phd for more information.

Delft University of Technology

Delft University of Technology (the TU Delft) is a multifaceted institution offering education and carrying out research in the technical sciences at an internationally recognised level. Education, research and design are strongly oriented towards applicability. The TU Delft develops technologies for future generations, focusing on sustainability, safety and economic vitality. At the TU Delft you will work in an environment where technical sciences and society converge. The TU Delft comprises eight faculties, unique laboratories, research institutes and schools.

https://www.tudelft.nl

Faculty Electrical Engineering, Mathematics and Computer Science

The Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) is known worldwide for its high academic quality and the social relevance of its research programmes. The faculty’s excellent facilities accentuate its international position in teaching and research. Within this interdisciplinary and international setting the faculty employs more than 1100 employees, including about 400 graduate students and about 2100 students. Together they work on a broad range of technical innovations in the fields of sustainable energy, telecommunications, microelectronics, embedded systems, computer and software engineering, interactive multimedia and applied mathematics.

The research at the Delft Institute of Applied Mathematics (DIAM) centers around the analysis of mathematical models arising in science and engineering. This research is both fundamental and applied in nature, and is often inspired by technical applications. The department plays an active role in translating research results into concrete, practical applications. It maintains intensive contacts with other TU Delft departments, the major technological institutes and the research laboratories of major companies. Within its own subject field, the department provides teaching for the Applied Mathematics BSc and MSc programmes, and also contributes to the teaching of mathematics courses within other academic programmes at TU Delft, and within national programmes such as “MasterMath”.

The Statistics group covers one of the key research areas at DIAM. It aims at developing theory within the field of mathematical statistics as well as applying state-of-the-art statistical theory to problems from practice. Within DIAM, there is close collaboration with the applied probability group, exemplified by a joint weekly seminar and joint educational efforts (basic probability and statistics courses and courses in the Finance minor and master tracks) and active participation in Delft Data Science (DDS). The Statistics Helpdesk constitutes an interesting interface with other disciplines present at the TU Delft, leading to new interesting statistical problems and appreciation of statistics by other research groups. The group is relatively small and communication lines are short. 

https://www.tudelft.nl/en/eemcs/the-faculty/