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Rapid Numerical Approximation Method for Integrated Covariance Functions Over Irregular Data Regions

In many practical applications, spatial data are often collected at areal levels (i.e., block data) and the inferences and predictions about the variable at points or blocks different from those at which it has been observed typically depend on integrals of the underlying continuous spatial process. In this paper we describe a method based on Fourier transform by which multiple integrals of covariance functions over irregular data regions may be numerically approximated with the same level of accuracy to traditional methods, but at a greatly reduced computational expense.