Automatic estimation of spatial spectra via smoothing splines

摘要

Spectra are frequently used to depict the dependence features of a second-order stationary process. In this paper, the spatial log-spectral density is expressed by a new type of smoothing splines in the form of the summation of a linear expression of univariate bases and two quadratic forms of univariate bases. Based on this new type of smoothing splines, a Bayesian nonparametric method is proposed to estimate the spectral density of spatial data observed on a lattice. The proposed Bayesian approach uses a Hamiltonian Monte Carlo-within-Gibbs technique to fit smoothing splines to the spatial periodogram. Our technique produces an automatically smoothed spatial spectral estimate along with samples from the posterior distributions of the parameters to facilitate inference.