Covariance tapering for likelihood based estimation in large spatial data sets

Cari Kaufman

Likelihood-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(n3) 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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