# RESEARCH: Statistics

The Department of Mathematics has an active group of researchers working in both theoretical and applied statistics, and related problems in probability theory. This work concerns the mathematical foundations of mathematical statistics, experimentation, and data analysis, including optimal design of experiments and optimal decision-making under various degrees of prior uncertainty. In addition we work on many real-world applications of this theory, including in the fields of engineering, computer science, cyber security, defense, medicine, and computational biology. In this regard, particularly, we benefit from close collaborations with other departments at USC including Electrical Engineering, Computer Science, the Information Science Institute, Computational Biology, USC Medical School, and NASA's Jet Propulsion Laboratory, as well as a variety of industry collaborations. Ph.D. students are trained in statistics through the department's Mathematics Ph.D. program, and the department offers professional master's degrees in Statistics and Math Finance as well. The department also runs a weekly Probability and Statistics seminar.

###### Faculty

- Jay Bartroff: Sequential analysis, multiple testing, optimal experimental design, Stein's method, and biomedical applications
- Larry Goldstein: Distributional approximation and Stein's method,sampling schemes in

epidemiology, statistical efficiency, optimal stopping. - Lei Li: Computational Biology and Genomics, Blind Inversion Problem
- Sergey Lototsky: Statistical Inference for Stochastic Differential Equations
- John Rolph: Statistics, Public Policy
- Alan Schumitzky: Probability and Statistics
- Fengzhu Sun (Dept. of Biology): Computational Biology, Statistical Genetics, Mathematical Modeling
- Alexander Tartakovsky: Theoretical and applied statistics, applied probability, sequential analysis, optimal stopping

###### Faculty in Related Areas

- Kenneth Alexander: Probability, Statistical Mechanics
- Richard Arratia: Probability, Combinatorics, Number Theory
- Peter Baxendale: Probability, Stochastic Differential Equations, Random Dynamical Systems
- Ting Chen: Analysis of Algorithms, Computational Biology
- Jason Fulman: Algebraic Combinatorics and Probability
- Gareth James (Dept. of Information & Operations Management): Functional Data Analysis and Statistical Learning Methods
- Edmond Jonckheere: Applied Topology/Geometry, Internet Traffic Signals Analysis
- Jinchi Lv (Dept. of Information & Operations Management): Variable Selection and Machine Learning
- Jin Ma: Stochastic Analysis, Stochastic Differential Equations, Stochastic Control Theory, Differential Equations, Mathematical Finance and Actuarial Sciences
- Gerard Medioni (Dept. of Computer Science): Image Understanding
- Remy Mikulevicius: Applied Mathematics, Stochastic Processes, Partial Differential Equations
- Peter Radchenko (Dept. of Information & Operations Management): High Dimensional Statistical Inference
- Simon Tavare: Statistics, Computational Biology, Stochastic Computation
- Michael Waterman (Dept. of Biology): Computational Biology, Probability, Statistics
- Jianfeng Zhang: Probability

###### Undergraduate Probability and Statistics Courses

- MATH 208x Elementary Probability and Statistic
- MATH 218 Probability for Business
- MATH 407 Probability Theory
- MATH 408 Mathematical Statistics

###### Graduate Probability Courses

- MATH 503 Stochastic Calculus for Finance
- MATH 505ab Applied Probability
- MATH 506 Stochastic Processes
- MATH 507ab Theory of Probability
- MATH 509 Stochastic Differential Equations

###### Graduate Statistics Courses

- MATH 511abL Data Analysis
- MATH 541ab Introduction to Mathematical Statistics
- MATH 542L Analysis of Variance and Regression
- MATH 543L Nonparametric Statistics
- MATH 544L Multivariate Analysis
- MATH 545L Introduction to Time Series
- MATH 546 Statistical Computing
- MATH 547 Methods of Statistical Inference
- MATH 548 Sequential Analysis
- MATH 550 Sample Surveys
- MATH 650 Seminar in Statistical Consulting

###### Graduate Computational Biology Courses

- MATH 577ab Computational Molecular Biology Laboratory
- MATH 578ab Computational Molecular Biology

###### Related Graduate Courses

- MATH 585 Mathematical Theory of Optimal Control
- MATH 601 Optimization Theory and Techniques