Statistics Department Hosts Weekly Colloquiums where reputed researchers and scholars in the field of statistics give presentations highlighting their work from academia, industry, and government agencies.

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.