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

我们推导了用于计算Vecchia高斯过程对数似然近似的梯度和Fisher信息的单遍算法，该算法为应用Fisher评分算法最大化对数似然提供了一种计算有效的手段。在数值示例中以及在对Argo海洋温度数据的应用中证明了优化技术的优势。与仅使用函数求值的优化方法相比，新方法可以更快，更可靠地找到最大似然估计，尤其是当协方差函数具有许多参数时。这使从业人员可以将非平稳模型拟合到大型时空数据集。