Graph-Based Approximation of Matérn Gaussian Fields
Ruiyi Yang, Princeton University
Matérn Gaussian fields (MGFs) have been popular modeling choices in many aspects of Bayesian methodologies. In this talk we will discuss a generalization of MGFs to manifolds and graphs. In the first part, we formalize the definition of MGFs on manifolds and introduce a sparse approximation based on graph discretization together with a convergence analysis, complementing the finite element approximations of MGFs on Euclidean domains. Numerical examples will demonstrate their wide applicability. In the second part, we introduce a framework for choosing the number of discretization nodes when approximating MGFs and demonstrate the ideas through the finite element approaches. We propose a conceptually simple selection rule and show that in many practical scenarios a low-rank finite element approximation is sufficient to further reduce computational cost without hindering the estimation accuracy.