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) provides international leadership in quantitative finance and insurance analytics.
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 contagion effects in financial networks by asymptotic methods facilitating random graphs. He is also working in the area of infinite-dimensional stochastic analysis and its applications to mathematical finance. This work includes infinite dimensional polynomial processes, Markovian representations for Stochastic Volterra equations, Heath-Jarrow-Morton models for energy markets and their calibration with neural networks. Nils Detering recently also worked on an interdisciplinary project with a colleague from the department of Psychological and Brain Sciences at UCSB. This project aims at modeling serotonergic fibers and their densities in the brain.
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.
Research interests include covariance estimation, Bayesian inference, sensitivity analysis, causal inference, and missing data. Application areas include the analysis of “omics” data, with a recent focus on proteomics, as well as applications in sports analytics with a focus on basketball.
Research interests include probabilistic models of multiple time series, images, spatio-temporal data and functional data, with emphasis on scalable computation and theoretical properties. His research projects broadly encompass topics in data science and machine learning, with applications in quantifying uncertain geological hazards, high-throughput material characterization, epidemic models, computer model emulation, and data inversion.
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.
Research interests include machine learning, financial mathematics, game theory, sequential experimental design, and systemic risk modeling. She is currently working on developing machine learning theory and algorithms for high-dimensional stochastic dynamical problems, with applications emphasizing finance, mean-field games, and pandemic models.
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.
Research interests include: probability, stochastic processes, stochastic differential equations, collisions of Brownian particles, local time of semimartingales, rough paths, signature, mathematical economics & finance (stochastic portfolio theory, mean-field game/control), data science in finance, molecular biology & sports.
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 mathematical finance, actuarial science, and stochastic modeling. Some topics of recent research are computational finance, Monte Carlo methods, stochastic games, high-frequency trading, longevity modeling, renewable energy generation, Gaussian Process surrogates in finance, stochastic simulation, and numeric methods for stochastic control. Dr. Ludkovski collaborates with statisticians, actuaries, operations researchers and engineers.
Research interests include: spatial/temporal data analysis, geophysical model evaluation, and functional data analysis in the environmental sciences.
Research interests include learning underlying relationships in large-scale data. Dr. Oh works on topics in inference, scalable computation, and high-performance software implementation for graphical models, and enjoys applying my research to genomic, financial, and neuroscience data.
Dr. Pedersen is interested in research in financial economics and its application to insurance. His primary practice area is economic scenario generation. Primary research interests include interest rate models and their estimation, credit risk, and insurance risk securitization.
Research interests include actuarial science, risk modeling, Applied Financial Modelling and Econometrics, DeFi and Blockchain, Statistics and Machine Learning, Statistical Signal Processing.
Recent topics have been Life Insurance modelling, usage-based insurance, cyber risk insurance, operational risk, environmental risk models and green finance and regulation and practice, Cryptocurrency markets, Spatial and Temporal statistics, heavy-tailed processes (alpha-stable), time-series modelling, Wireless sensor network models.
As an educator, Dr. Ravat is interested in Probabilistic thinking, Introductory Statistics and Data science education and outreach activities that promote diversity in STEM fields and Data Science spaces. She also pursues research in the area of Stochastic Optimization and Game Theory.
Research interests include smoothing spline, mixed-effects models, model selection, survival data, longitudinal data, computational statistics, statistical software, microarray data analysis and biostatistical modeling.
Research interests include high-dimensional statistics, multiple testing problems, graphical models, and convex optimization.
JOSEPH GANI (In Memoriam)
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.
DAVID V. HINKLEY (In Memoriam)
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