Kryging: geostatistical analysis of large-scale datasets using Krylov subspace methods

Analyzing massive spatial datasets using a Gaussian process model poses computational challenges. This is problem prevailing heavily in applications such as environmental modeling, ecology, forestry and health. We present novel approximate inference methodology that uses profile likelihood Krylov subspace methods to estimate the covariance parameters makes predictions with uncertainty quantification for point-referenced data. “Kryging” combines Kriging applies both observations on regular grid irregularly spaced observations, any stationary isotropic (and certain geometrically anisotropic) function, including popular Matérn family. make use of block Toeplitz structure blocks matrix fast Fourier transform bypass memory bottlenecks approximating log-determinant matrix-vector products. perform extensive simulation studies show effectiveness our by varying sample sizes, parameter values sampling designs. A real data application also performed dataset consisting land surface temperature readings taken MODIS satellite. Compared existing methods, proposed method performs satisfactorily much less computation time better scalability.