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

Speaker: Professor Andrew Fowlie (Nanjing Normal University)

Time: 13:30pm, July 09, 2021

Location: 3-302, PMO Xianlin Campus

Abstract: We propose a novel method for computing pp-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 \log^2{1/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.