RESUMEN
Physical theories that depend on many parameters or are tested against data from many different experiments pose unique challenges to statistical inference. Many models in particle physics, astrophysics and cosmology fall into one or both of these categories. These issues are often sidestepped with statistically unsound ad hoc methods, involving intersection of parameter intervals estimated by multiple experiments, and random or grid sampling of model parameters. Whilst these methods are easy to apply, they exhibit pathologies even in low-dimensional parameter spaces, and quickly become problematic to use and interpret in higher dimensions. In this article we give clear guidance for going beyond these procedures, suggesting where possible simple methods for performing statistically sound inference, and recommendations of readily-available software tools and standards that can assist in doing so. Our aim is to provide any physicists lacking comprehensive statistical training with recommendations for reaching correct scientific conclusions, with only a modest increase in analysis burden. Our examples can be reproduced with the code publicly available at Zenodo.
RESUMEN
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 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.
