2022 journal article
Bayesian spatial modeling using random Fourier frequencies
SPATIAL STATISTICS, 48.
Spectral methods are important for both theory and computation in spatial data analysis. When data lie on a grid, spectral approaches can take advantage of the discrete Fourier transform for fast computation. If data are not on a grid, then low-rank processes with Fourier basis functions may be sufficient approximations. However, deciding which basis functions to use is difficult and can depend on unknown parameters. Here, we introduce Bayesian Random Fourier Frequencies (BRFF), a fully Bayesian extension of the random Fourier features approach. BRFF treats the spectral frequencies as random parameters, which unlike fixed frequency approximations allows the frequencies to be data-adaptive and averages over uncertainty in frequency selection. We apply this method to non-gridded continuous, binary, and count data. We compare BRFF using simulated and observed data to another popular low-rank method, the predictive processes (PP) model. BRFF is faster than PP, and outperforms or matches the predictive performance of the PP model in settings with high numbers of observations.