Statistical Theory & Methodology
Faculty members engage in foundational research in statistical theory, including asymptotic inference, nonparametric estimation, and the development of new statistical methodologies. This work provides the theoretical underpinnings for various applied statistical techniques.
Applied Statistics in Environmental and Biomedical Sciences
The department applies statistical methods to a range of real-world problems in environmental sciences, biology, and biomedicine. Research includes the analysis of complex datasets to address issues such as ecological modeling, public health, and genetic studies.
Interdisciplinary Collaborations
The department fosters interdisciplinary research, collaborating with other departments and institutions in areas like computer science, economics, and engineering. These collaborations aim to apply statistical expertise to diverse scientific and technological challenges.
Financial Mathematics
Through the Center for Financial Mathematics and Actuarial Research (CFMAR), faculty explore quantitative finance topics like asset pricing, risk management, and derivatives modeling. Actuarial science research focuses on insurance analytics and risk assessment.
Actuarial Science
Faculty members engage in theoretical, methodological and applied areas of Actuarial Science including: general insurance, cyber risk and insurance, life insurance, mortality modelling and demographics, health insurance, life insurance, pensions and annuities, fixed income and term risks, long dated actuarial liability modelling, machine learning, predictive analytics and statistical applications in actuarial sciences and quantitative risk management. This work provides core foundations for translation of research into actuarial practice.
UCSB PSTAT is proud to be named a leader in actuarial education, earning its status as a Center of Actuarial Excellence (CAE) from the Society of Actuaries in 2022, as well as being a Gold Partner with the Casualty Actuarial Society.
Stochastic Processes & Applied Probability
Research in this area includes the study of stochastic differential equations, random processes, and their applications to fields such as finance, physics, and engineering. Faculty investigate the behavior of systems under uncertainty and develop probabilistic models.
The major research areas of our department can be divided into theoretical statistics and statistical methodology, applied statistics, and probability. Our faculty members are actively engaged in interdisciplinary research in such areas as mathematics, computer science, biostatistics, environmental sciences, and financial mathematics and statistics. These dynamic interactions with researchers in other disciplines are both personal, through joint projects supported by the NSF, NIH, and other government agencies, and through the activities of the DataLab situated in the Department.
The Department also hosts Center for Financial Mathematics and Actuarial Research (CFMAR) which provides national and international leadership in quantitative finance. Its research activities are directed toward study of financial markets, asset prices, risk management, investment strategies, derivatives pricing and hedging, and systemic risk among other topics.
Our faculty’s applied statistics research spans a wide range of fields including environmental sciences, different biological and biomedical fields, population genetics, and finance.
Research Areas of Special Emphasis
Theoretical Statistics and Statistical Methodology
- Bayesian inference & computational methods
- Bayesian networks
- Resampling techniques
- Directional data analysis
- Functional data analysis
- Data mining
- Computational statistics
- Nonparametric inference
- Asymptotic statistical methods
- Linear models and generalized linear models
- Smoothing spline methods
- Time series and spatial/temporal data models
- Mixed effects models
Probability
- Stochastic processes
- Stochastic control
- Sequential detection
- Interacting particle systems
Financial Mathematics
- Systemic risk in financial market
- Stochastic games
- Stochastic portfolio theory
- Stochastic volatility modeling
- Risk management and Actuarial Applications
Actuarial Science and Insurance Mathematics
- Insurance Mathematics
- Mortality Modelling and Demographic Statistics
- General Insurance and Reserving Methods
- Life Insurance and Annuities
- Quantitative Risk Management
- Risk Measures
- Fairness and Insurance Pricing
- Actuarial Applications
- Interest Rate modelling and Fixed Income
- Time Series Methods
- Machine Learning and Predictive Analytics
Time Series, Forecasting and Econometrics
- Time Series Methods Estimation and Inference
- Time Series Regression
- Time Series Structural Change and Change Point Detection methods
- Multivariate Time Series models: Cointegration, Panel Regregression, MIDAS, Functional Regression State Space Modelling
- Filtering Linear and Non-Linear Systems
- Machine Learning and Predictive Analytics
- Applications in Time Series Analysis
Applied Statistics
- Environmental statistics
- Ecological statistics
- Geophysical statistics
- Statistical education
- Image data analysis
- Spatial statistics
Biostatistics
- Survival analysis
- Clinical trials
- Longitudinal data analysis
- Bayesian methods for Biosurveillance
- Stochastic modeling of biomedical events