  Covariance tapering is a popular approach for reducing the computational cost
of spatial prediction and parameter estimation for Gaussian process models.
However, tapering can have poor performance when the process is sampled at
spatially irregular locations or when non-stationary covariance models are
used. This work introduces an adaptive tapering method in order to improve the
performance of tapering in these problematic cases. This is achieved by
introducing a computationally convenient class of compactly supported
non-stationary covariance functions, combined with a new method for choosing
spatially varying taper ranges. Numerical experiments are used to show that the
performance of both kriging prediction and parameter estimation can be improved
by allowing for spatially varying taper ranges. However, although adaptive
tapering outperforms regular tapering, simply dividing the data into blocks and
ignoring the dependence between the blocks is often a better method for
parameter estimation.
