Title: Bayesian Nonparametric Spectral Estimation,
Abstract: 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 this https URL.