2nd May 2024 Debashis Mondal (University of Washington in St Louis)

Title: Matrix-free Conditional Simulation of Gaussian Random Fields
Abstract: In recent years, interest in spatial statistics has increased significantly. However, for large data sets, statistical computations for spatial models have remained a challenge, as it is extremely difficult to store a large covariance or an inverse covariance matrix and compute its inverse, determinant, or Cholesky decomposition. In this talk, we shall focus on spatial mixed models and discuss a new algorithm for fast matrix-free conditional samplings for their inference. This new algorithm relies on `rectangular' square roots of the inverse covariance matrices and covers a large class of spatial models including spatial models based on Gaussian conditional and intrinsic autoregressions, and fractional Gaussian fields. We shall show that the algorithm outperforms sparse Cholesky and other existing conditional simulation methods. We demonstrate the usefulness of this algorithm by analyzing groundwater arsenic contamination in Bangladesh, and by analyzing environmental bioassays from the New York-New Jersey harbor area. Part of this work is done in collaboration with Somak Dutta at Iowa State University.
Bio: Debashis Mondal is an associate professor at the Department of Statistics and Data Science, at Washington University. Prior to joining Washington University, he was on the statistics faculty at Oregon State University and the University of Chicago. He received his PhD in statistics from the University of Washington. Mondal's research interests include Spatial statistics, computational science, and machine learning; applications in ecology (including microbial ecology) and environmental sciences. He is a recipient of the NSF Career Award, the Young Researcher Award, and the inaugural Junior Service Award by the International Indian Statistical Association and is an elected member of the International Statistical Institute.