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, 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 Keck 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

  • Larry Goldstein: Stein’s method in statistics and distributional approximation, concentration inequalities, sampling schemes, mathematical molecular biology, and optimal stopping
  • Sergey Lototsky: Statistical Inference for Stochastic Differential Equations
  • Jinchi Lv (joint w/ Marshall School of Business): Statistics, machine learning, data science, business applications, and artificial intelligence and blockchain
  • Stanislav (Stas) Minsker: Statistical learning theory, high-dimensional statistics, and closely related topics from probability theory including empirical processes and concentration-of-measure inequalities
  • Mohamed (Simo) Ndaoud: High dimensional probability and statistics; in particular, variable selection, support recovery and community detection in the high dimensional setting
  • Dmitrii Ostrovskii: Statistics, large-scale optimization, and machine learning
  • Alan Schumitzky (Emeritus): Probability and Statistics
  • Fengzhu Sun (Dept. of Biology): Computational Biology, Statistical Genetics, Mathematical Modeling
  • Michael Waterman (Dept. of Biology): Computational Biology, Probability, Statistics

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
  • 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
  • Remi 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
  • Jianfeng Zhang: Math finance

Current Graduate Students

  • Maria Allayioti (Goldstein/Bartroff)
  • Chinmoy Bhattacharjee (Goldstein)
  • Apoorva Shah (Lototsky)
  • Lijia (Coco) Wang (Bartroff)
  • Wayne Walker (Goldstein)
  • Hao Wu (Lv/Zhang)
  • Shunan Yao (Minsker/Tong)

Recently Graduated Ph.D. Students

  • 2022
    • Jinting Liu (Bartroff/Sun)
    • Apoorva Shah (Lototsky)
    • Hao Wu (Lv/Zhang)
  • 2021
    • Wang, Lang (Minsker)
    • Luo, Jiajun (Minsker)
  • 2020
    • Aronowitz, Julian (Bartroff). First position: Data Scientist, Palo Alto Networks
    • He, Xinrui (Bartroff). First position: Data Scientist, Google
  • 2019
    • Demirkaya, Emre (Yingying Fan/Goldstein/Lv), Reproducible Large-Scale Inference in High-Dimensional Nonlinear Models. First position: Assistant Professor, University of Tennessee Haslam College of Business.
    • He, Xinrui (Bartroff), Asymptotically optimal sequential multiple testing with (or without) prior information on the number of signals. First position: Statistician at Acumen LLC/The SPHERE Institute.
    • Wei, Xiaohan (Minsker/Neely), High-dimensional estimation under weak moment assumptions. First position: Research Scientist at Facebook.
    • Wiroonsri, Nathakhun (Goldstein), Stein’s Method via Approximate Zero Biasing and Positive Association with Applications to the Combinatorial Central Limit Theorem and Statistical Physics. First position: Lecturer at King Mongkut’s University of Technology, Thailand, Department of Mathematics.
  • 2018
    • Bhattacharjee, Chinmoy (Goldstein), Stein’s Method and its Applications in Strong Embeddings and Dickman Approximations. First position: Postdoctoral Fellow at University of Bern, Switzerland.
    • Kim, Hyun-Jung (Lototsky), Time-Homogeneous Parabolic Anderson Model.
    • Wang, Jian (Lototsky), Statistical Inference For Second-Order Ordinary Differential Equation Driven by Additive Gaussian White Noise.
  • 2017
    • Hankin, Michael (Bartroff), Sequential Testing of Multiple Hypotheses With FDR Control under Dependence. First position: Statistician at Google.
  • 2016
    • Tsilifis, Panagiotis (Ghanem/Mikulevicius), Design, adaptation and variational methods in Uncertainty Quantification. First position: Postdoc in the Viterbi School of Engineering at USC.
  • 2015
    • Zheng, Zemin (Goldstein/Lv), High-Dimensional Latent Variable Thresholded Regression. First position: Assistant Professor at the Chinese University of Science and Technology.
  • 2014
    • Bessam, Diogo (Lototsky), Large Deviations Rates in a Gaussian Setting and Related Topics. First position: Postdoc at PUC-RJ/IMPA (Brasil).
    • Sokolov, Grigory (Tartakovsky/Lototsky), Multi-Population Optimal Change-Point Detection. First position: Postdoc at SUNY Binghamton.
  • 2013
    • Chubatiuk, Alona (Schumitzky), Nonparametric Estimation of an Unknown Probability Distribution Using Maximum Likelihood and Bayesian Approaches. First position: Postdoc at Children’s Hospital LA.
    • Song, Jinlin (Bartroff), Time-Sequential Testing for Multiple Hypotheses. First position: Analyst at The Analysis Group, Boston.
    • Xu, Li (Lototsky), Parameter Estimate for Hyperbolic SPDE’s with Stochastic Coefficients. First position: Google.
    • Zhong, Jie (Lototsky), Second Order in Time Stochastic Evolution Equation and Wiener Chaos Approach. First position: Postdoc at Ritsumeikan University (Japan).
  • 2012
    • Ghosh, Subhankar (Goldstein), Couplings for Berry-Esseen Bounds and Concentration Inequalities. First position: SAS Statistical Software.
    • Kaligotla, Sivaditya (Lototsky), Asymptotic Problems in Stochastic Partial Differential Equations: A Wiener Chaos Approach. First position: Bloomberg LP.
    • Lin, Ning (Lototsky), Estimation of Coefficients in Stochsatic Differential Equations. First position: Citigroup.
    • Moers, Michael (Lototsky), Statistical Inference of Stochastic Differential Equations Driven by Gaussian Noise. First position: Deutsche Bank.
    • Xu, Shanshan (Lototsky/Wilcox), Initiative Non-Parametric Multivariate Regression Hypothesis Testing.
  • 2011
    • Lin, Wei (Goldstein), Survival Analysis With Missing Data and High Dimensionality. First position: Postdoc at University of Pennsylvania.

Undergraduate Probability and Statistics Courses

  • MATH 114 Foundations of Statistics
  • MATH 208x Elementary Probability and Statistic
  • MATH 218 Probability for Business
  • MATH 307 Statistical Inference and Data Analysis I
  • MATH 308 Statistical Inference and Data Analysis II
  • 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