Xiangping Hu

Xiangping Hu (Department of Mathematics, Uio),

gives a seminar in our usual Auditorium 4 at 14:15, Tuesday Nov. 5'th:

Title: New approach for multivariate Gaussian random fields

Abstract: We discuss how to construct multivariate GRFs and
multivariate GRFs with oscillating covariance functions
with systems of Stochastic Partial Differential Equations
(SPDEs). By solving a system of SPDEs, we can construct
multivariate GRFs. On the theoretical side, the notorious
requirement of non-negative definiteness for the covariance
matrix of the GRF is satisfied since the constructed
covariance matrices with this approach are automatically
symmetric positive definite. Using the approximate stochastic
weak solutions to the systems of SPDEs, multivariate
GRFs are represented by multivariate Gaussian Markov
random fields (GMRFs) with sparse precision matrices.
Therefore, on the computational side, the sparse structures
make it possible to use numerical algorithms for sparse
matrices to do fast sampling from the random fields and
statistical inference. Some examples will be given in order
to illustrate how to use the newly proposed approach.