# Hierarchical Bayesian Level Set Inversion

arXiv: https://arxiv.org/abs/1601.03605 · HTML: https://mlsanity.com/paper/1601.03605/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jan 2016.

## Built on by (most cited first, 6 of 6)

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- [Efficient Deconvolution in Populational Inverse Problems](https://mlsanity.com/paper/2505.19841/) (2025)
- [A Novel Cluster Classify Regress Model Predictive Controller Formulation; CCR-MPC](https://mlsanity.com/paper/2101.07655/) (2021)
- [Deep Adaptive Dimension Reduction for Bayesian Inference in Inverse Problems](https://mlsanity.com/paper/2605.29373/) (2026)
- [Flow Matching for Fast Posterior Sampling in Bayesian Inverse Problems](https://mlsanity.com/paper/2610.02377/) (2026)

## Abstract (arXiv)

The level set approach has proven widely successful in the study of inverse problems for interfaces, since its systematic development in the 1990s. Recently it has been employed in the context of Bayesian inversion, allowing for the quantification of uncertainty within the reconstruction of interfaces. However the Bayesian approach is very sensitive to the length and amplitude scales in the prior probabilistic model. This paper demonstrates how the scale-sensitivity can be circumvented by means of a hierarchical approach, using a single scalar parameter. Together with careful consideration of the development of algorithms which encode probability measure equivalences as the hierarchical parameter is varied, this leads to well-defined Gibbs based MCMC methods found by alternating Metropolis-Hastings updates of the level set function and the hierarchical parameter. These methods demonstrably outperform non-hierarchical Bayesian level set methods.