Areas of Excellence

Some of the areas of excellence in our department include:

• (AM) Mathematical biology: Professor Marc Mangel works on mathematical modeling of biological phenomena, especially the evolutionary ecology of growth, aging, and longevity; quantitative issues in fishery management; mathematical and computational aspects of disease). Associate Professor Hongyun Wang works on modeling of protein motors, with applications to nanotechnology, theoretical biophysics, energy transduction mechanism of protein motors; thermodynamics of small systems; partial differential equations; statistical physics; classical analysis and numerical analysis.
• (S) Bayesian nonparametric methods: One important wave of the future in Bayesian methods is nonparametrics, which involves placing probability distributions on functions (the statistics of the 21st century) rather than on scalars or vectors (the statistics of the 18th through 20th centuries). Professor David Draper works on this and other topics, including Bayesian hierarchical modeling, stochastic optimization, Markov chain Monte Carlo methods, model uncertainty, quality assessment in health and education, risk assessment and applications in the social and environmental sciences. Assistant Professor Athanasios Kottas works on Bayesian nonparametric modeling and inference, mixture models, probability order constraints, quantile regression, spatial statistics, and survival analysis. Assistant Professor Abel Rodríguez also works on Bayesian nonparametric modeling and inference, financial econometric models and statistical models for genomic and protemic data.
• (AM) Fluid mechanics: Assistant Professor Pascale Garaud works on mathematical modeling of natural flows, numerical solutions of differential equations, planetary formation, and internal dynamics of stars with applications to astrophysics and geophysics. Associate Professor Nic Brummell works on fluid dynamics, compressible convection, magnetohydrodynamics, turbulence, dynamos and other highly nonlinear systems; numerical methods, simulations and supercomputing. Nic Brummell and Pascale Garaud are both members of TASC (Theoretical Astrophysics at Santa Cruz).
• (S) Computationally intensive Bayesian inference, prediction, and decision-making: Modern methods of Bayesian statistics employ Markov chain Monte Carlo (MCMC) techniques to draw inferences and make predictions and decisions. These methods are highly computationally intensive, and are crucial to the continued success of the Bayesian approach in applied problem-solving. Associate Professor Herbie Lee works on computational methods, inverse problems, computer models, spatial inverse problems, machine learning, model selection and model averaging. Associate Professor Raquel Prado works on Bayesian analysis of nonstationary time series, multivariate time series, biomedical signal processing, wavelets, statistical models for genomic data. Professor David Draper is also involved in this area.
• (AM, S) Envirometrics: Professor Marc Mangel studies population biology of disease and quantitative fishery science. Associate Professor Bruno Sanso works on Bayesian predictive modeling of environmental variables in space and time, statistical inference from climate model output, Bayesian spatial modeling, modeling of changes in atmospheric variables and geostatistical applications.