Mode Collapse in Nested Sampling

2026/06/22 by Johannes Buchner · 2 voices
Mathematics · Physics and Astronomy · #stat.CO #astro-ph.IM

paper · pdf

Abstract

Nested Sampling is a Monte Carlo algorithm enabling posterior estimation and Bayesian model comparison, and is especially robust in multi-modal posteriors. This is because nested sampling maintains a population of live points sampled from the entire prior. In each iteration, the population is advanced above a likelihood threshold, potentially discarding modes ruled out by the data. However, the Monte Carlo nature of point replenishment can also accidentally discard a mode. We draw a connection to the neutral Moran process in genetics, and quantify the occurrence probability of this failure mode of nested sampling with a simple symmetric random walk model on the live point occupancy. We find a simple rule for setting the minimum number of live points so that mode die-out is made unlikely.

Citations

• Snowballing Nested Sampling
• Nested sampling for physical scientists
• UltraNest -- a robust, general purpose Bayesian inference engine
• A statistical test for Nested Sampling algorithms
• Properties of Nested Sampling
• Multimodal nested sampling: an efficient and robust alternative to MCMC methods for astronomical data analysis
• Random processes in genetics

Discussions

• Johannes Buchner: Mode Collapse in Nested Sampling https://arxiv.org/abs/2606.22929 https://arxiv.org/pdf/2606.22929 https://arxiv.org/html/2606.22929 [bsky, 1 points, 0 comments]
• This paper arxiv.org/abs/2606.22929 makes a connection between genetics and nested sampling's spawning of a new live points from existing live point population. [bsky, 0 points, 1 comments]

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