Proximal nested sampling with data-driven priors for physical scientists

2023/06/30 by Jason D. McEwen, T.I Liaudat, McEwen, Jason D. +7 · 1 citation
Computer Science · Mathematics · #FOS: Computer and information sciences #FOS: Physical sciences #Gaussian Processes and Bayesian Inference #Instrumentation and Methods for Astrophysics (astro-ph.IM) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Methodology (stat.ME) #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2307.00056

openalex publication_date 2023/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Bayesian model selection and misspecification testing in imaging inverse problems only from noisy and partial measurements

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