Parallel inference for massive distributed spatial data using low-rank models

In both cases, the challenge is to obtain valid inference that does not require processing all data at a single central computing node.

We show that for a very widely used class of spatial low-rank models, which can be written as a linear combination of spatial basis functions plus a fine-scale-variation component, parallel spatial inference and prediction for massive distributed data can be carried out exactly, meaning that the results are the same as for a traditional, non-distributed analysis. The communication cost of our distributed algorithms does not depend on the number of data points.