Gaussian process learning via Fisher scoring of Vecchia’s approximation

We derive a single-pass algorithm for computing the gradient and Fisher information of Vecchia’s Gaussian process loglikelihood approximation, which provides computationally efficient means applying scoring maximizing loglikelihood. The advantages optimization techniques are demonstrated in numerical examples an application to Argo ocean temperature data. new methods find maximum likelihood estimates much faster more reliably than method that uses only function evaluations, especially when covariance has many parameters. This allows practitioners fit nonstationary models large spatial spatial–temporal datasets.