The department’s research expertise ranges from theoretical probability and statistics to advanced applied data analysis techniques, computational statistics, and financial mathematics and statistics. This is reflected in the curriculum, which prepares undergraduate and graduate students for careers in the insurance, financial and pharmaceutical industries. Many of our graduate students go on to careers in academia as faculty members in universities around the world.
The use of statistics in many disciplines provides an opportunity for inter-disciplinary collaboration between the Department of Statistics and Applied Probability and other departments on campus. Our faculty members are actively engaged in interdisciplinary research in such areas as mathematics, computer science, biostatistics, environmental sciences, and financial mathematics and statistics. The Statistical Laboratory (Statlab) provides the entire UCSB campus with access to expertise in data-analysis methodology, experimental and study design, and statistical computation. At the same time, the Statlab trains Statistics graduate students in statistical consulting. The Center for Financial Mathematics and Actuarial Research (CFMAR) opened its doors in Fall 2006 to provide international leadership in quantitative finance from different point of view. These programs provide multiple learning opportunities for both graduate students and faculty.
Faculty Research Interests
Our faculty members each bring a unique perspective to the department and have widely varying interests, specialties, and expertise. Specifically, our faculty’s research interests are as follows:
Research interests include: asymptotic statistical inference, comparisons of statistical experiments, density estimation and nonparametric function estimation.
Research interests include: stochastic differential equations with non-Gaussian noises, time series, filtering problems.
Research interests include stochastic processes, stochastic partial differential equations, waves in random media, financial mathematics.
Dr. Holmes’ Research interests include: the maximum entropy formalism and Bayesian networks, data mining, foundations of Bayesianism, Brouwer’s programme and intuitionistic mathematics, issues in statistics education.
Dr. Hsu continues to work on Bayesian estimation of covariance matrices. The Bayesian estimation for the linear mixed effects models, with a very flexible prior structure, has been fully developed. He is also working on a project of Bayesian methods in estimating ordered mortality rates. The project is interesting, however, the computation is challenging due to the constraints of the parameters.
Dr. Ichiba's research interests include: probability, stochastic processes, stochastic differential equations, collisions of Brownian particles, local time of semimartingales, mathematical economics & finance (stochastic portfolio theory), and statistics in finance, molecular biology & sports.
Dr. Jammalamadaka's research interests include a wide range of topics such as nonparametric methods, large sample theory, tests and efficiencies, directional data, censoring, spacings and goodness-of-fit methods. He is also investigating machine-learning tools and pattern recognition for high-dimensional data.
Research interests include: stochastic control, especially as applied to financial mathematics and insurance models, optimal stopping theory, control problems with partial information, Monte Carlo methods.
Research interests include: spatial/temporal data analysis, geophysical model evaluation, and functional data analysis in the environmental sciences.
Research interests include: smoothing spline, mixed-effects models, model selection, survival data, longitudinal data, computational statistics, statistical software, microarray data analysis and biostatistical modeling.
Dr. Gani has been working on an ecological model for a plantation-nursery system, as well as some epidemic models for SARS and the spread of HIV by infected syringe needles. He has also written on the development of Statistics at the Australian National University since 1952.
Research interests include: resampling methods, model selection, nonparametric curve fitting, comparisons between objective Bayes and frequentist inference.
SVETLOZAR T. RACHEV
Stability of stochastic models, mathematical and empirical finance