Research

Several of our faculty members are interested in applying probabilistic methods to the modeling, analysis, and control of stochastic systems that arise in business, economics, engineering, and statistics. Such methods include stochastic dynamic programming, queuing theory, empirical processes, point processes, limit theorems, large deviations, and concentration of measure phenomena.

We are very active in decision theory and decision analysis, where the focus is on modeling decisions under uncertainty, ranging from decisions faced by individuals (e.g., whether or not to have surgery) to those faced by large corporations (e.g., whether to shift manufacturing to China) to public policy decisions (e.g., how to deal with nuclear waste or set environmental standards). Research in the area is similarly broad. For instance, it includes foundational work involving axioms of rational behavior and the implications of these axioms. It also includes the structuring and representing uncertainty (probability modeling, scoring rules to evaluate probabilities, Bayesian statistics, forecasting) and of preferences (utility theory, conflicting objectives, multiattribute utility). The analysis of decision-making problems within this stream of research (particularly sequential decision-making problems and competitive problems) draws on areas such as optimization, dynamic programming, and game theory.

There has been a tremendous growth of available data from emerging new technologies. In turn, this leads to new (high-dimensional) models with a large number of parameters to be estimated. Related applications include recommendation systems for online retailers, measuring the impact of thousands of different genes on the propensity for diseases using data from a few hundred patients, controlling for many social economic variables to allow for the proper estimation of the impact of policy variables, pharmacovigilance accounting for health records of patients, and understanding interactions within social networks. Such high-dimensional estimations are increasingly common in biostatistics, business, economics, and signal processing. Our faculty members are active in developing new related methodologies and research questions.

While the field of mechanism design was originated in the economic theory literature, during the past decade researchers have extended the methodology and found an array of uses and applications ranging from screening customers/agents to improve the system performance, or maximizing revenues in digital advertising. This research is interdisciplinary in nature and intersects with computer science, operations management and operations research. Our faculty develop new methodologies that handle important and practically relevant aspects of emerging complex business environments and its market participants, e.g. the role of budget constraints, externalities, impact of networks, limited liability, simultaneous and sequential market-clearing, etc. In particular, market design (where one optimizes market rules before it is created) and dynamic mechanism design (where the information is revealed and participants interact multiple times over time) have become increasingly central topics of research in this area.

Optimization theory and dynamic programming has a long tradition in operations research. The faculty of the Decision Sciences area have contributed to the theory of optimization and dynamic programming, as well as to their use in many applied problems. Several aspects have been investigated, ranging from the computational complexity of algorithms to the numerical implementation to specific applications. In particular, convex optimization, integer programming and relaxation techniques have been extensively studied and applied by members of the group. These tools are also relevant in the analysis of a variety of different problems in other streams of research.