Covariance Tapering in Spatial Statistics
نویسنده
چکیده
In the analysis of spatial data, the inverse of the covariance matrix needs to be calculated. For example, the inverse is needed for best linear unbiased prediction or kriging, and is repeatedly calculated in the maximum likelihood estimation or the Bayesian inferences. Since the spatial sample size can be quite large, operations on the large covariance matrix can be a numerical challenge if not impossible. A natural idea is to make the covariances exactly zero after certain distance so that the resulting matrix has a high proportion of zero entries and is therefore a sparse matrix. Operations on sparse matrices take up less computer memories and run faster. However, this has to be done in a way such that the resulting matrix is still positive definite. Covariance tapering assures that the tapered covariance matrix is positive definite while retaining most of the information.
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