Large spatial data sets are now ubiquitous in environmental science. Fine spatial sampling or many observations across large domains provides a wealth of information and can often address new scientific questions. However, the richness and scale of large datasets often reveal heterogeneity in spatial processes that add more complexity to a statistical analysis. A strategy for handling larger problems is to rely on separate local analyses of the data but with a view to combine the results into a seamless global model. In this talk two examples are presented for handling the simulation and uncertainty quantification of non-stationary Gaussian processes. The global model in this case is a process convolution of a white noise field where the convolution function varies across space. Such a model is difficult to implement explicitly for large spatial fields. In this case local fitting is used to estimate spatially varying covariance parameters and these are encoded into a sparse Markov random field model for a global representation. This strategy makes it possible to estimate and then simulate (unconditional) non-stationary Gaussian processes. A different approach can be exploited for conditional simulation of a spatial field to quantify the uncertainty of spatial predictions. If the local window for conditional simulation is chosen appropriately one can generate seamless conditional fields that approximate solving the global problem. The unconditional method is illustrated for the emulation of surface temperature fields from an ensemble of climate model experiments (Community Earth System Model Large Ensemble) and the conditional method is used to generate an ensemble from the analysis of space-time observations from ocean drifter buoys ( ARGO profiling floats).
References for background reading:
Nychka, Douglas, Soutir Bandyopadhyay, Dorit Hammerling, Finn Lindgren, and Stephan Sain. “A multiresolution Gaussian process model for the analysis of large spatial datasets.” Journal of Computational and Graphical Statistics 24, no. 2 (2015): 579-599.
Alexeeff, Stacey E., Doug Nychka, Stephan R. Sain, and Claudia Tebaldi. “Emulating mean patterns and variability of temperature across and within scenarios in anthropogenic climate change experiments.” Climatic Change (2016): 1-15.