  Proximal nested sampling was introduced recently to open up Bayesian model
selection for high-dimensional problems such as computational imaging. The
framework is suitable for models with a log-convex likelihood, which are
ubiquitous in the imaging sciences. The purpose of this article is two-fold.
First, we review proximal nested sampling in a pedagogical manner in an attempt
to elucidate the framework for physical scientists. Second, we show how
proximal nested sampling can be extended in an empirical Bayes setting to
support data-driven priors, such as deep neural networks learned from training
data.
