# Bayesian Nonparametric Spectral Estimation

arXiv: https://arxiv.org/abs/1809.02196 · HTML: https://mlsanity.com/paper/1809.02196/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Sep 2018.

## Built on by (most cited first, 6 of 6)

- [Nonstationary multi-output Gaussian processes via harmonizable spectral mixtures](https://mlsanity.com/paper/2202.09233/) (2022)
- [Marginalising over Stationary Kernels with Bayesian Quadrature](https://mlsanity.com/paper/2106.07452/) (2021)
- [Online Probabilistic Model Identification using Adaptive Recursive MCMC](https://mlsanity.com/paper/2210.12595/) (2022)
- [Gaussian process deconvolution](https://mlsanity.com/paper/2305.04871/) (2023)
- [Computationally-efficient initialisation of GPs: The generalised variogram method](https://mlsanity.com/paper/2210.05394/) (2022)
- [JIR-Arena: The First Benchmark Dataset for Just-in-time Information Recommendation](https://mlsanity.com/paper/2505.13550/) (2025)

## Abstract (arXiv)

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.