## Covariance tapering for likelihood based estimation in large spatial data setsCari KaufmanSAMSI/NCAR AbstractLikelihood-based methods such as maximum likelihood, REML, and Bayesian methods are attractive approaches to estimating covariance parameters in spatial models based on Gaussian processes. Finding such estimates can be computationally infeasible for large datasets, however, requiring O(n ^{3}) calculations for each evaluation
of the likelihood based on n observations. I will discuss the method of covariance
tapering to approximate the likelihood in this setting. In this approach, covariance
matrices are "tapered," or multiplied element-wise by a compactly supported
correlation matrix. This produces matrices which can be be manipulated using
more efficient sparse matrix algorithms. I will present two approximations to
the Gaussian likelihood using tapering and discuss the asymptotic behavior of
estimators maximizing these approximations. I will also present an example of using
the approximations in a Bayesian model for the climatological (long-run mean)
temperature difference between two sets of output from a computer model of global
climate, run under two different land use scenarios.
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