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arXiv · 2606.22929

Mode Collapse in Nested Sampling

Johannes Buchner
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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.

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Johannes Buchner. 2026-06-22. Mode Collapse in Nested Sampling. https://arxiv.org/abs/2606.22929

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