PhD Position Mathematical Statistics

The Department of Applied Mathematics in the Faculty of Electrical Engineering, Mathematics and Computer Science at Delft University of Technology is seeking a hardworking PhD candidate.

Job description

The goal of this position is to advance the state of the art and develop new theory and methodology for dependence models, in particular copula-based statistical models. Since the 1990s, copulas have become recognized as the main tool to model arbitrary dependence (not necessarily linear) between random variables, with applications in many quantitative fields, including finance and risk management, insurance, hydrology, and health.

This project consists of three main research directions.

1. The first subproject is related to recent developments in the theory of conditional copulas and conditional dependence models. These models quantify the influence of a random vector X on the dependence between two random variables Y1 and Y2 of interest, or more. This has applications in particular in finance where some leading financial assets can influence the dependence between other assets. The goal is to recover the structure underlying a set of estimated conditional dependence functions, with a generalization towards conditional U-statistics.
2. The second subproject is to develop a theory of information geometry for copulas. Information geometry is a field at the interface between probability, statistics and geometry, and aims at getting geometrical information and structure on statistical problems, for example quantifying angles and directions in the space of probability measures, here in the space of copulas.
3. The third subproject is to integrate discrete random variables into the Pair-Copula Bayesian Networks (PCBNs) and develop a structure learning algorithm. PCBN models allow one difficult problem, the inference of a multivariate distribution or density, to be decomposed into smaller bivariate problems by using information on conditional independencies. Contrary to classical Gaussian Bayesian networks, the approach here relies on copulas with arbitrary margins.

These three projects are mostly independent and can be done in any order, also depending on the preferences of the successful candidate.

Job requirements

• You hold or will soon complete an MSc degree in Mathematical Statistics or equivalent.
• You have experience with programming in R. Experience with compiled languages such as C++ is a plus.
• You have high-level mathematical skills and are curious to invent new models and theories.
• You are fluent in English, both spoken and written.

About TU Delft

Delft University of Technology is a top international university combining science, engineering and design. It delivers world class results in education, research and innovation to address challenges in the areas of energy, climate, mobility, health and digital society.

Faculty of Electrical Engineering, Mathematics and Computer Science

The Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) brings together three scientific disciplines. Combined, they reinforce each other and are the driving force behind the technology we use in daily lives. The faculty works on areas including sustainable electricity grids, future chips and sensors, software technologies including AI, and applied mathematics research such as mapping disease processes using single cell data and simulating volcanic ash plumes. There is plenty of room for ground-breaking research, supported by excellent labs and facilities in a strong international environment.

Conditions of employment

Doctoral candidates will be offered a 4-year period of employment in principle, in the form of two employment contracts. An initial 1.5-year contract includes an official go/no go progress assessment within 15 months, followed by an additional contract for the remaining 2.5 years assuming performance requirements are met.

As a PhD candidate you will be enrolled in the TU Delft Graduate School. The TU Delft Graduate School provides an inspiring research environment with an excellent team of supervisors, academic staff and a mentor. The Doctoral Education Programme is aimed at developing your transferable, discipline-related and research skills.

TU Delft offers a customisable compensation package, discounts on health insurance, and a monthly work costs contribution. Flexible work schedules can be arranged.