Nonparametric Bayesian inference for the spectral density based on irregularly spaced data

Various approaches for spectral analysis based on regularly spaced data have already been well-established, but the spectral inference based on irregularly spaced data are still essentially limited. Under the Bayesian framework, a detouring approach for spectral estimation is proposed for analyzing irregularly spaced data. The detouring process is accomplished by three steps: (1) normalizing the data in some sense on frequency domain by a time-scale change, (2) estimating the spectral density of the time-scale changed process, and (3) solving the estimated spectrum by the relation of spectral densities between the model and its time-scale-changed version. The proposed approach uses a Hamiltonian Monte Carlo-within Gibbs technique to fit smoothing splines to the periodogram. Our technique produces an automatically smoothed spectral estimate. The time-scale-change not only allows basis functions in the smoothing splines to be independent of sampling design, but also makes the proposed estimation need not to adjust tuning parameters according to different irregularly spaced data. (C) 2020 Elsevier B.V. All rights reserved.