B0351
Title: Adaptive finite element type decomposition of Gaussian random fields
Authors: Debdeep Pati - Texas A&M University (United States) [presenting]
Abstract: A general class of approximate Gaussian processes (GP) obtained is investigated by taking a linear combination of compactly supported basis functions with the basis coefficients endowed with a sparse dependence structure. This general class includes two highly scalable approximate GP methods: the finite element approximation of the stochastic partial differential equation associated with Matern GP and a linear approximation of a general GP on a regular lattice. Prior distributions are proposed for the number of basis functions to yield the optimal rate of posterior convergence of the underlying function, adaptively over a large class of smoothfunctions. Two scalable algorithms and numerics are also provided to illustrate the methodology.
