Proximal nested sampling for high-dimensional Bayesian model selection

Abstract Bayesian model selection provides a powerful framework for objectively comparing models directly from observed data, without reference to ground truth data. However, requires the computation of marginal likelihood (model evidence), which is computationally challenging, prohibiting its use in many high-dimensional inverse problems. With imaging applications mind, this work we present proximal nested sampling methodology compare alternative that images inform decisions under uncertainty. The based on sampling, Monte Carlo approach specialised comparison, and exploits Markov chain techniques scale efficiently large problems tackle are log-concave not necessarily smooth (e.g., involving $$\ell _1$$ ?1 or total-variation priors). proposed can be applied dimension $${\mathcal {O}}(10^6)$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">O(106) beyond, making it suitable It validated Gaussian models, available analytically, subsequently illustrated range where used analyse different choices dictionary measurement model.