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 $\log^2{1/p}$, which compares favorably to the $1/p$ scaling for Monte Carlo (MC) simulations. For significances greater than about $4\sigma$ 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 $5\sigma$ 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.
翻译:我们建议一种基于嵌套抽样(NS)计算美元价值的新方法,该方法适用于抽样空间,而不是问题参数空间,与巴伊西亚计算时的用法相反。NS比额表的计算成本为$=log2{2{{1/p}美元,与蒙特卡洛(MC)模拟的1/p美元比例值相比,优于蒙特卡洛(MC)模拟的1/p美元比例值。对于玩具问题和简化共振搜索中超过4美元的价值,我们表明NS要求的模拟数量比普通MC估计少。这与高能物理特别相关,高能物理采用5\sigma$的黄金标准进行发现。我们最后谈到Bayesian和常客计算之间的新联系,以及调整NS实施的可能性,以便在这一环境下进行更好的业绩。