  Gaussian processes are popular and flexible models for spatial, temporal, and
functional data, but they are computationally infeasible for large datasets. We
discuss Gaussian-process approximations that use basis functions at multiple
resolutions to achieve fast inference and that can (approximately) represent
any spatial covariance structure. We consider two special cases of this
multi-resolution-approximation framework, a taper version and a
domain-partitioning (block) version. We describe theoretical properties and
inference procedures, and study the computational complexity of the methods.
Numerical comparisons and an application to satellite data are also provided.
