# Proximal nested sampling with data-driven priors for physical scientists

arXiv: https://arxiv.org/abs/2307.00056 · HTML: https://mlsanity.com/paper/2307.00056/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 31 references that are in the map.
- First posted on arXiv 30 Jun 2023.

## Builds on (most cited first, 13 of 13)

- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [Generative Modeling by Estimating Gradients of the Data Distribution](https://mlsanity.com/paper/1907.05600/) (2019)
- [Improved Techniques for Training Score-Based Generative Models](https://mlsanity.com/paper/2006.09011/) (2020)
- [Improving Diffusion Models for Inverse Problems using Manifold Constraints](https://mlsanity.com/paper/2206.00941/) (2022)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [Noise2Score: Tweedie's Approach to Self-Supervised Image Denoising without Clean Images](https://mlsanity.com/paper/2106.07009/) (2021)
- [Bayesian imaging using Plug & Play priors: when Langevin meets Tweedie](https://mlsanity.com/paper/2103.04715/) (2021)
- [Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau](https://mlsanity.com/paper/1612.07471/) (2016)
- [Proximal Markov chain Monte Carlo algorithms](https://mlsanity.com/paper/1306.0187/) (2013)
- [Proximal nested sampling for high-dimensional Bayesian model selection](https://mlsanity.com/paper/2106.03646/) (2021)
- [Machine learning assisted Bayesian model comparison: learnt harmonic mean estimator](https://mlsanity.com/paper/2111.12720/) (2021)

## Built on by (most cited first, 4 of 4)

- [Improving Gradient-guided Nested Sampling for Posterior Inference](https://mlsanity.com/paper/2312.03911/) (2023)
- [Differentiable and accelerated spherical harmonic and Wigner transforms](https://mlsanity.com/paper/2311.14670/) (2023)
- [Bayesian model selection and misspecification testing in imaging inverse problems only from noisy and partial measurements](https://mlsanity.com/paper/2510.27663/) (2025)
- [Quenched Ensemble Sampling](https://mlsanity.com/paper/2609.15894/) (2026)

## Abstract (arXiv)

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.