The Department of Mathematics and Statistics has experts working across diverse areas of probability and statistics.

- The department’s statistical expertise spans the field’s theoretical, computational, and applied aspects. A sampling of specialties includes computational methods for big data, Bayesian inference, high-dimensional statistics, causal inference, and inference for discrete structures such as networks, statistical and machine learning among many others. Various faculty apply statistics in neuroscience, bioinformatics, finance, and many other disciplines.
- The department’s probability expertise spans the field’s theoretical, computational, and applied aspects. Specialties include stochastic processes, stochastic analysis, limit theorems, Malliavin calculus, random matrix theory, non-commutative probability, computational probability, multiscale methods like averaging and homogenization, large deviations, metastability and stochastic partial differential equations.

The group is also strongly connected to the applied mathematics and dynamics groups within the department. The group organizes the Statistics and Probability Seminar.

**Faculty:**

- Yves Atchade: Markov Chain Monte Carlo for high-dimensional Bayesian (or quasi-Bayesian) inference, stochastic methods in optimization, and remote sensing data to study social and environmental issues in Africa.
- Solesne Bourguin: Markov diffusion operators and Dirichlet forms, Malliavin calculus and regularity of laws, Stein’s method and limit theorems, non-commutative probability theory and its combinatorial aspects
- Luis Carvalho: Bayesian and computational statistics, statistical machine learning, Objective Bayes, network analysis, high-dimensional discrete inference. Applications in transportation studies, environmental studies (remote sensed data), and bioinformatics.
- Julio Castrillon: uncertainty quantification, machine and statistical learning, non-linear stochastic networks, (non-linear) stochastic partial differential equations, and anomaly detection. Applications to protein interactions, power systems (electric grid), deforestation (Amazons), and genomics.
- Uri Eden: developing mathematical and statistical methods to analyze neural spiking activity
- Ashis Gangopadhyay: modeling volatility of financial time series, change-point identification in financial time series, nonparametric and semiparametric methods
- Mamikon Ginovyan: prediction, estimation, and hypotheses testing
- Jonathan Huggins: computational statistics, Bayesian statistics, trustworthy machine learning, large-scale learning and inference, genomic data analysis, ecological modeling
- Mark Kon: quantum probability and information, bioinformatics, machine and statistical learning, mathematical physics, mathematical and computational neuroscience, complexity theory, and wavelets
- Varsha Kulkarni
- Judith Lok: causality, counterfactuals, longitudinal data, observational studies, competing risks, survival analysis, HIV/AIDS, personalized medicine, mediation analysis, clinical trial design
- Mickey Salins: probability theory, random processes, stochastic partial differential equations, large deviations
- Debarghya Mukherjee: asymptotic theory of high dimensional statistics, theoretical analysis of non-standard asymptotics and application of statistical methods in machine learning
- Konstantinos Spiliopoulos: algorithmic and computational methods in machine and statistical learning, applied mathematics, stochastic processes and probability, financial mathematics, asymptotic problems for stochastic processes and (stochastic) partial differential equations such as multiscale methods and large deviations, statistical analysis, network modeling and statistical inference
- Emily Stephen: statistical modeling of neural signals at different spatial scales
- Daniel Sussman: statistics for network data, node embeddings, graph matching, causal inference under interference, brain networks, molecular networks, social networks, knowledge graphs
- Haviland Wright
- Daniel Weiner: limit theorems in probability and statistics; history of mathematics.
- Masanao Yajima: multivariate analysis, hierarchical model, multiple comparison, statistical computing, missing, data imputation, network modeling, bioinformatics (metagenomics, proteomics, transcriptomics), large data, research reproducibility

**PhD Students:
**

- Ante Bing
- Dan Cunha
- Likun (Lily) Chou
- Scott Douthit
- Haoyue Feng
- Yudong Feng
- Kelly Geyer
- Azar Ghahari
- Calvin Guan
- Wan-Chi Hsin
- Man Huang
- Luis Iberico
- Keer Jiang
- Hangcheng Lai
- Jiawei Li
- Jingjing Li
- Xinru Liu
- Vindyani Herath Mudiyanselage
- Hancong Pan
- Yi Sun
- Liang Wang
- Liwei Wang
- Yu Wang
- Manushi Welandawe
- Shiwen Yang
- Sirui Zeng
- Qiuyun Zhu