Statistics and Operations Research
Modern statistics encounters the new challenges that science and industry bring to its door, where the traditional statistical problems have exploded both in size and complexity. Analyzing complex high-dimensional data requires novel approaches and techniques. Research on Big Data problems combines methodological study of high-dimensional inference, model selection, statistical learning and data mining with development of statistical and computational tools for their practical applications. A special focus is given on applications in statistical genetics and bioinformatics.
Selective and simultaneous inference, also known as Multiple Comparisons, is another major research topic at the Department. It is of special current importance because selective inference is inherent in Big Data analysis. The emphasis has been on the “False Discovery Rate” (FDR), a widely used concept that has its origins in the Department. Several research projects are being carried out to extend FDR’s theoretical and practical use in model selection, brain imaging, and genomics problems. More generally, our concern is about the replicability problem in the Life Sciences that are hindered by selective inference problems, research supported by a large ERC grant. The Department also participates in the European Human Brain Project, where strategies are developed for scientific data mining of medical information that incorporate the above concerns.
Much of the current research on design of experiments has been directed toward experiments with non-standard outcomes. This includes binary and Poisson responses and computer experiments, in which a computer simulator replaces the test bench as the venue for exploring a scientific question. Sequential design of binary experiments has been applied to the area of sensitivity tests, which estimate the quantiles of a dose-response probability curve.
The research in continuous optimization focuses on the theoretical foundations of optimization, and the design and complexity analysis of algorithms for solving huge scale optimization problems which arise in a variety of diverse scientific areas ranging from communication systems, signal recovery, finance, imaging sciences and machine learning to mention just a few. It includes convex and non-smooth analysis, first order and proximal methods, convex relaxations, operator splitting techniques, variational methods, robust optimization and stochastic approximations.
Research topics in combinatorial optimization include design of approximation algorithms for NP-hard problems, location theory, network flows, sub-modular function optimization, and online algorithms .
Research in the stochastic part of Operations Research focuses on Queueing Theory, including polling systems, Jackson-type networks, retrial systems and batch-service models. Reliability theory and communication networks are also among the topics studied. Another major area of research is economics of queues, in particular strategic behavior in queueing systems.
The research in game theory and mathematical economics that is conducted in the department is quite diversified.
The main topics we study are:
1. Non-cooperative games, including dynamic games with various information structures, stochastic games, stopping games (in discrete and continuous time), games with vector-payoffs, dynamic programming, auction theory, mechanism design, solution concepts, and interactive epistemology.
2. Informational and knowledge aspects of decisions under uncertainty.
3. Topics in microeconomics, including general equilibrium implementation and equity.
4. Algorithmic game theory, including combinatorial auctions and complexity issues.
5. Cooperative games, including Nash bargaining problem, matching, bankruptcy problems, and market games.
Statistical and probabilistic methods related to biological and genetics applications are a major focus of the research performed in our department.
Among the areas being investigated are:
- Developing statistical methodologies for analyzing genome-wide association studies (GWAS)
- Addressing fundamental issues in collection, management and analysis of biological data, including lack of replicability, control of false discovery, and effective management of shared data resources
- Developing probabilistic models to address important problems in areas like systems biology, population genetics and speciation