应用似然函数比以及Fourier变换计算置信度的解析方法

新粒子寻找的实验结果要通过计算置信度来解释,置信度的定义或是基于新粒子与本底并存的假设,或是基于唯有本底存在的假设.通常的计算方法是产生大量的toy Monte Carlo实验,这些实验按照某种定义的估计值的大小以顺序排列,然后将真正观测到的实验的估计值与之相比较,从而得到置信度.本文则介绍一种新的计算方法,通过定义似然函数比为实验的估计值,并应用Fourier变换,用解析的方法计算出置信度,与toy Monte Carlo方法相比,解析方法可极大地提高计算的速度和精度.

Analytic Confidence Level Calculations Using the Likelihood Ratio and Fourier Transform

The interpretation of new particle search results involves a confidence level calculation on either the discovery hypothesis or the background-only("null")hypothesis. A typical approach uses toy Monte Carlo experiments to build an expected experiment estimator distribution against which an observed experiment's estimator may be compared. In this note, a new approach is presented which calculates analytically the experiment estimator distribution via a Fourier transform, using the likelihood ratio as an ordering estimator. The analytic approach enjoys an enormous speed advantage over the toy Monte Carlo method, making it possible to quickly and precisely calculate confidence level results.