Statistical Models and Methods Based on Stochastic Partial Differential Equations
This talk presents an overview of our research on statistical methods using stochastic partial differential equations (SPDEs), focusing on non-Gaussian random fields and fractional-order SPDEs, and theory for random fields and statistical analysis on metric graphs, highlighting theoretical contributions, software development, and applications relevant to KAUST RDI pillars.
Overview
In this talk, I will give an overview of the research of my group in the broad area of statistical methods based on stochastic partial differential equations (SPDEs). This research is in the interface between statistics, probability, applied mathematics and numerical analysis and I will in particular focus on three main areas. I will first discuss the creation of flexible non-Gaussian random fields based on SPDEs and corresponding computationally efficient methods for statistical inference and robustness analysis. I will then introduce our work on computationally efficient methods for statistical modeling based on fractional-order SPDEs. Finally, I will present our ongoing work on creating a complete theory for random fields and statistical analysis on metric graphs. In all three areas, we have made significant theoretical contributions and developed user-friendly and well-documented softwares that increase the impact of the research by facilitating researchers to use the methods in a wide range of applications. A few of these applications will be highlighted throughout the talk to illustrate the relevance for the KAUST RDI pillars.
Presenters
Brief Biography
David Bolin is an associate professor of statistics in the CEMSE Division at KAUST, where he leads the Stochastic Processes and Applied Statistics research group. Before joining KAUST, he was an associate professor of Mathematical Statistics at the University of Gothenburg. He received his Ph.D. in mathematical statistics from Lund University in 2012.
Bolin's research focuses on stochastic partial differential equations (SPDEs) and their applications in statistics, with an emphasis on developing practical, computationally efficient tools for modeling non-stationary and non-Gaussian processes. He has made significant contributions to the theory of Gaussian processes, optimal linear prediction, fractional-order SPDEs, and stochastic processes on metric graphs. He has also developed and maintains several widely used software packages for advanced statistical modeling.
Bolin serves as an associate editor for the Scandinavian Journal of Statistics, is an elected member of the International Statistical Institute, and has received multiple honors, including the Section on Statistics and the Environment Early Investigator Award from the American Statistical Association and the Cramér Prize from the Cramér section of the Swedish Statistical Society.
