The Third Competition on Spatial Statistics for Large Datasets

Given the computational challenges involved in calculating the maximum likelihood estimates for large spatial datasets, there has been significant interest in the research community regarding approximation methods for estimation and subsequent predictions. However, prior studies examining the evaluation of these methods have primarily focused on scenarios where the data are observed on a regular grid or originate from a uniform distribution of locations. Nevertheless, non-uniformly distributed locations are commonplace in fields like meteorology and ecology. Examples include gridded data with missing observations acquired through remote sensing techniques. To assess the reliability and effectiveness of cutting-edge approximation methods, we have initiated a competition focused on estimation and prediction for large spatial datasets with non-uniformly distributed locations. Participants were invited to employ their preferred methods to generate corresponding confidence and prediction intervals for synthetic datasets of varying sizes and spatial configurations. This competition serves as a valuable opportunity to benchmark and compare different approaches in a controlled setting. We evaluated the submissions from 11 different research teams worldwide. In summary, the Vecchia approximation and the fractional SPDE methods were among the best performers for estimation and prediction. Furthermore, the nearest neighbors Gaussian process and the multi-resolution approximation exhibited excellent performance in predictive tasks. These findings provide valuable guidance for selecting the most appropriate approximation methods based on specific data characteristics. Supplementary materials accompanying this paper appear online.