Mixture of noises and sampling of non-log-concave posterior distributions
Résumé
This work considers a challenging radio-astronomy
inverse problem of physical parameter inference from multispec-
tral 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
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