Proximal nested sampling with data-driven priors for physical scientists

TL;DR

This paper reviews proximal nested sampling for high-dimensional Bayesian model selection in imaging and extends it to incorporate data-driven priors like neural networks, making it more applicable to real-world problems.

Contribution

It provides a pedagogical review of proximal nested sampling and introduces an extension to empirical Bayes with data-driven priors for physical sciences.

Findings

Proximal nested sampling effectively handles high-dimensional models with log-convex likelihoods.

Extension to data-driven priors enables the use of neural networks learned from data.

The framework is suitable for Bayesian model selection in computational imaging.

Abstract

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.