Mixture of noises and sampling of non-log-concave posterior distributions

This work considers a challenging radio-astronomy inverse problem of physical parameter inference from multispectral observations. The forward model underlying this problem is a computationally expensive numerical simulation. In addition, the observation model mixes different sources of noise yielding a non-concave log-likelihood function. To overcome these issues, we introduce a likelihood approximation with controlled error. Given the absence of ground truth, parameter inference is conducted with a Markov chain Monte Carlo (MCMC) algorithm to provide credibility intervals along with point estimates. To this aim, we propose a new sampler that addresses the numerical challenges induced by the observation model, in particular the non-log-concavity of the posterior distribution. The efficiency of the proposed method is demonstrated on synthetic yet realistic astrophysical data. We believe that the proposed approach is very general and can be adapted to many similar difficult inverse problems.