Approximations of Markov Chains and High-Dimensional Bayesian Inference

Jonathan Christopher  Mattingly grew up in Charlotte, NC where he attended Irwin Ave elementary and Charlotte Country Day.  He graduated from the NC School of Science and Mathematics and received a BS is Applied Mathematics with a concentration in physics from Yale University. After two years abroad with a year spent at ENS Lyon studying nonlinear and statistical physics on a Rotary Fellowship, he returned to the US to attend Princeton University where he obtained a PhD in Applied and Computational Mathematics in 1998. After 4 years as a Szego assistant professor at Stanford University and a year as a member of the IAS in Princeton, he moved to Duke in 2003. He is currently a Professor of Mathematics and of Statistical Science.

His expertise is in the longtime behavior of stochastic system including randomly forced fluid dynamics, turbulence, stochastic algorithms used in molecular dynamics and Bayesian sampling, and stochasticity in biochemical networks.

Since 2013 he has also been working to understand and quantify gerrymandering and its interaction of a region's geopolitical landscape. This has lead him to testify in a number of court cases including in North Carolina, which led to the NC congressional and both NC legislative maps being deemed unconstitutional and replaced for the 2020 elections. 

He is the recipient of a Sloan Fellowship and a PECASE CAREER award.  He is also a fellow of the IMS and the AMS. He was awarded the Defender of Freedom award by  Common Cause for his work on Quantifying Gerrymandering.

My research focuses on developing new tools for probabilistic learning from complex data - methods development is directly motivated by challenging applications in ecology/biodiversity, neuroscience, environmental health, criminal justice/fairness, and more.  We seek to develop new modeling frameworks, algorithms and corresponding code that can be used routinely by scientists and decision makers.  We are also interested in new inference framework and in studying theoretical properties of methods we develop.  

Some highlight application areas: 
(1) Modeling of biological communities and biodiversity - we are considering global data on fungi, insects, birds and animals including DNA sequences, images, audio, etc.  Data contain large numbers of species unknown to science and we would like to learn about these new species, community network structure, and the impact of environmental change and climate.

(2) Brain connectomics - based on high resolution imaging data of the human brain, we are seeking to developing new statistical and machine learning models for relating brain networks to human traits and diseases.

(3) Environmental health & mixtures - we are building tools for relating chemical and other exposures (air pollution etc) to human health outcomes, accounting for spatial dependence in both exposures and disease.  This includes an emphasis on infectious disease modeling, such as COVID-19.

Some statistical areas that play a prominent role in our methods development include models for low-dimensional structure in data (latent factors, clustering, geometric and manifold learning), flexible/nonparametric models (neural networks, Gaussian/spatial processes, other stochastic processes), Bayesian inference frameworks, efficient sampling and analytic approximation algorithms, and models for "object data" (trees, networks, images, spatial processes, etc).