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.

翻译：近端嵌套采样方法最近被提出，旨在为计算成像等高维问题打开贝叶斯模型选择的大门。该框架适用于对数凸似然模型——这类模型在成像科学中普遍存在。本文目的有二：其一，以教学方式系统回顾近端嵌套采样框架，力求为物理学家阐明该体系；其二，展示如何在经验贝叶斯框架下扩展近端嵌套采样，使其支持数据驱动先验，例如从训练数据中学习的深度神经网络。