## Research areas

The Department has a long-standing tradition of excellence in research in probability, statistics and theoretical economics. Its recent expansion to the areas of data science, machine learning and mathematical analysis has further strengthened the Department’s intellectual breadth and diversity of its community of scholars.

Some of Decision Sciences Department themes are investigated by the Department in collaboration with the Bocconi Institute of Data Science and Analytics and with the Innocenzo Gasparini Institute of Economic Research.

The research activities may be broadly traced back to the following, closely related, subject areas:

Research on the foundations of Bayesian inference at Bocconi date back to the seventies thanks to the pioneering contributions of D.M. Cifarelli and E. Regazzini. Since then, research has expanded in many directions, including asymptotic statistics, Bayesian nonparametrics, discrete random structures, high-dimensional inference, statistical optimal transport, stochastic processes and uncertainty quantification.

Research in this area, motivated by challenging applied problems, investigates the core methodologies and principles of statistical and machine learning with emphasis on modeling, computation and uncertainty quantification. Cutting-edge contributions have been given to computational statistics (e.g. MCMC, SMC, variational methods),

information theory, interpretable AI, network science, predictive inference, sensitivity analysis, statistical machine learning and computational social sciences.

Research in this area involves theoretical and applied aspects in various fundamental fields of Mathematical Analysis.

Tools of measure theory and calculus of variations, functional and non-smooth analysis, convex optimization are used and developed to study optimal transport problems (both from the theoretical and numerical point of view, also in the recent unbalanced and entropic forms), the differential-geometric structure of the space of probability measures, metric Sobolev spaces and measure-valued harmonic maps, spaces with lower Ricci curvarture bounds, partial differential equations, gradient flows and rate-independent problems, mean field planning and optimal control.

Research in these areas is devoted to the development of the mathematical and theoretical foundations of models in economics. This has led to important contributions to: consumer theory, dynamical systems, game theory, mathematical economics, network analysis and optimization.

The area is focused on developing mathematical models for decision making and risk assessment. Relevant contributions have been provided to: agent-based simulation, decision and risk analysis and sensitivity analysis.