Probabilistic and statistical modeling and its applications are key focus areas at the CICS. Research in probability theory and stochastic processes include stochastic PDEs, nonlinear filtering and data assimilation techniques, measure-valued processes, spatial statistics, stochastic control theory, probabilistic approaches to PDEs, stability and the qualitative theory of stochastic dynamical systems, modeling of rare events, and the theory of large deviations.
Focus areas include Monte Carlo simulation including Sequential Monte Carlo and Particle Filter methods, Gibbs measures and phase transitions, non-parametric statistics, variational methods, as well as stochastic/probabilistic networks. Significant research is conducted on numerical methods for stochastic dynamical systems, Markov chain approximations, and spectral and collocation methods.
Particular statistical topics of relevance to many application domains include the development of Bayesian emulators/surrogate models, generative implicit models for high-dimensional data, information-theoretic techniques for coarse-graining including the identification of collective variables and their dynamics, experimental design approaches, and modeling of rare events.