Bayesian Inference for High-Dimensional Nonstationary Gaussian Processes
A software package is developed that enables off-the-shelf functionality for conducting fully Bayesian analysis for general classes of nonstationary Gaussian process models, which are an extremely popular tool in spatial and environmental statistics as well as machine learning and emulation of complex mathematical and physical models.
Our software package provides data analysis tools that, for the first time, allow statisticians and data scientists to conduct data-driven interpolation and uncertainty quantification via formal Bayesian analysis for general classes of non-stationary Gaussian processes. Furthermore, we develop methods that are scalable to large data sets that can be implemented on a personal laptop and do not require a custom computing environment.
In spite of the diverse literature on nonstationary spatial modeling 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 a methodology for implementing formal Bayesian inference for a general class of nonstationary GPs. Our novel approach uses preexisting 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