Robust Bayesian spectral analysis via MCMC sampling
In this paper, the harmonic retrieval problems in white Gaussian noise, non-Gaussian impulsive noise and in presence of threshold observations are addressed using a Bayesian approach. Bayesian models are proposed that allow us to define posterior distributions on the parameter space. All Bayesian inference is then based on these distributions. Unfortunately, a direct evaluation of these latters and of their features requires evaluation of some complicated high-dimensional integrals. Efficient stochastic algorithms based on Markov chain Monte Carlo methods are presented to perform Bayesian computation. In simulation, these algorithms are able to estimate the unknown parameters in highly degraded conditions.