Bayesian Spectral Analysis with Student-t Noise
IEEE Transactions on Signal Processing
Institute of Electrical and Electronics Engineers (IEEE)
This is the author accepted manuscript. The final version is available from Institute of Electrical and Electronics Engineers (IEEE) via the DOI in this record.
We introduce a Bayesian spectral analysis model for one-dimensional signals where the observation noise is assumed to be Student-t distributed, for robustness to outliers, and we estimate the posterior distributions of the Student-t hyperparameters, as well as the amplitudes and phases of the component sinusoids. The integrals required for exact Bayesian inference are intractable, so we use variational approximation. We show that the approximate phase posteriors are Generalised von Mises distributions of order 2 and that their spread increases as the signal to noise ratio decreases. The model is demonstrated against synthetic data, and real GPS and Wolf’s sunspot data.
Vol. 62, Iss. 11, pp. 2871 - 2878