Space and Space-Time Modeling using Process Convolutions

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A continuous spatial model can be constructed by convolving a very simple, perhaps independent, process with a kernel or point spread function. This approach for constructing a spatial process offers a number of advantages over specification through a spatial covariogram. In particular, this process convolution specification leads to computational simplifications and easily extends beyond simple stationary models. This paper uses process convolution models to build space and space-time models that are flexible and able to accommodate large amounts of data. Data from environmental monitoring is considered.