2021/01/18 by L. Xia, Xia, Li-Gang, Zhang, Yan
Computer Science · #Algorithms and Data Compression #Bayesian Methods and Mixture Models #Blind Source Separation Techniques #Data Analysis #FOS: Physical sciences #High Energy Physics - Experiment (hep-ex) #Statistics and Probability (physics.data-an)
paper · pdf · doi:10.48550/arxiv.2101.06944
openalex publication_date 2021/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we attempt to refine the classic asymptotic formulae to describe the probability distribution of likelihood-ratio statistical tests. The idea is to split the probability distribution function into two parts. One part is universal and described by the asymptotic formulae. The other part is case-dependent and is estimated explicitly using a 6-bin model proposed in this work. The latter is similar to performing toy simulations and can therefore predict the discrete structures in the probability distributions. The new asymptotic formulae provide a much better differential description of the test statistics. This improved performance is demonstrated in two toy examples for common likelihood ratio statistics.