Bayesian Nonparametric Spectral Estimation
This work addresses uncertainty handling in spectral estimation for time series analysis, representing an incremental improvement over existing methods like Lomb-Scargle.
The paper tackles the problem of spectral estimation from partial and noisy observations by proposing a Bayesian nonparametric model that treats it as an exact inference problem, resulting in an analytic posterior distribution for the spectrum and efficient optimization of the power spectral density.
Spectral estimation (SE) aims to identify how the energy of a signal (e.g., a time series) is distributed across different frequencies. This can become particularly challenging when only partial and noisy observations of the signal are available, where current methods fail to handle uncertainty appropriately. In this context, we propose a joint probabilistic model for signals, observations and spectra, where SE is addressed as an exact inference problem. Assuming a Gaussian process prior over the signal, we apply Bayes' rule to find the analytic posterior distribution of the spectrum given a set of observations. Besides its expressiveness and natural account of spectral uncertainty, the proposed model also provides a functional-form representation of the power spectral density, which can be optimised efficiently. Comparison with previous approaches, in particular against Lomb-Scargle, is addressed theoretically and also experimentally in three different scenarios. Code and demo available at https://github.com/GAMES-UChile/BayesianSpectralEstimation.