In spite of the diverse literature on nonstationary spatial modelling and approximate Gaussian process (GP) methods, there are no general approaches for conducting fully Bayesian inference for moderately sized nonstationary spatial data sets on a personal laptop. For statisticians and data scientists who wish to conduct posterior inference and prediction with appropriate uncertainty quantification, the lack of such approaches and software is a limitation. Here, we develop methodology for implementing formal Bayesian inference for a general class of nonstationary GPs. Our novel approach uses pre-existing frameworks for characterizing nonstationarity in a new way while utilizing via modern GP likelihood approximations. Posterior sampling is implemented using flexible MCMC methods, with nonstationary posterior prediction conducted as a post-processing step. We demonstrate our novel methods on two data sets, ranging from several hundred to several thousand locations. All of our methods are implemented in the freely available BayesNSGP software package for R.

中文翻译：

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高维非平稳高斯过程的贝叶斯推理

尽管关于非平稳空间建模和近似高斯过程 (GP) 方法的文献多种多样​​，但没有在个人笔记本电脑上对中等大小的非平稳空间数据集进行完全贝叶斯推理的通用方法。对于希望通过适当的不确定性量化进行后验推理和预测的统计学家和数据科学家来说，缺乏此类方法和软件是一个限制。在这里，我们开发了为一般类别的非平稳 GP 实施形式贝叶斯推理的方法。我们的新方法使用预先存在的框架以新的方式表征非平稳性，同时利用现代 GP 似然近似。使用灵活的 MCMC 方法实现后验采样，将非平稳后验预测作为后处理步骤进行。我们在两个数据集上展示了我们的新方法，范围从数百到数千个位置。我们所有的方法都在 R 的免费 BayesNSGP 软件包中实现。