Karhunen-Loeve Expansion and Optimal Low-Rank Model for Spatial Processes
Department of Statistics
Karhunen-Loeve expansion has been well-studied in theory
and applied in mathematics, physics, engineering, hydrology and other
disciplines. It has found recent applications in the analysis of
massive spatial data when the exact likelihood function becomes
numerically intractable due to the large covariance matrix.
Karhunen-Loeve expansion results in an optimal approximation to the
underlying spatial process by a low-rank model, and makes the analysis
of massive spatial data feasible. However, we find that some
well-adopted algorithms for calculating the eigenvalues and
eigenfunctions do not work satisfactorily for spatial processes due to
either the speed or the precision. I will introduce some new algorithms
and compare their performances. I will also show some examples where we
used the KL expansion for statistical estimation and prediction.