Nested Sampling for Frequentist Computation: Fast Estimation of Small p -Values

Andrew Fowlie*, Sebastian Hoof, Will Handley

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


We propose a novel method for computing p-values based on nested sampling (NS) applied to the sampling space rather than the parameter space of the problem, in contrast to its usage in Bayesian computation. The computational cost of NS scales as log21/p, which compares favorably to the 1/p scaling for Monte Carlo (MC) simulations. For significances greater than about 4σ in both a toy problem and a simplified resonance search, we show that NS requires orders of magnitude fewer simulations than ordinary MC estimates. This is particularly relevant for high-energy physics, which adopts a 5σ gold standard for discovery. We conclude with remarks on new connections between Bayesian and frequentist computation and possibilities for tuning NS implementations for still better performance in this setting.

Original languageEnglish
Article number021801
JournalPhysical Review Letters
Issue number2
Publication statusPublished - 14 Jan 2022
Externally publishedYes


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