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Abstract:
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Fitting large spatial datasets using traditional geostatistical methods is often infeasible because some of the operations required to evaluate the likelihood are O(n^3). A common workaround is to approximate Gaussian processes with low-rank models using basis functions. If the data lie on a grid, spectral methods using Fourier basis functions and the Fast Fourier Transform (FFT) work particularly well. However, if the data are not on a grid, current spectral methods cannot be applied. Here, we introduce a new method that treats the Fourier frequencies as parameters. This allows us to recover the Gaussian process via Monte Carlo integration, meaning we do not have to rely on the restrictive pre-defined form of FFT frequencies. We apply this method to non-gridded univariate and multivariate continuous, binary, and count data. We compare our method to another popular low rank approximation, the predictive process model. Our new method outperforms the predictive process model in binary and count data settings.
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