Perturbation Theory and Mixture Models: Application to High-energy Physics

• Activity Number: 242
• Type: Invited
• Date/Time: Tuesday, August 9, 2005 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Cyrus C. Taylor*+ and Catherine Loader and Ramani S. Pilla
• Companies: Case Western Reserve University and Case Western Reserve University and Case Western Reserve University

Abstract

One of the fundamental problems in the analysis of experimental data is determining the statistical significance of a putative signal. Such a problem can be cast in terms of classical ``hypothesis testing," where a null hypothesis describes the background and an alternative hypothesis characterizes the signal as a perturbation of the background. This testing problem often is addressed by a chi-square goodness-of-fit or a likelihood ratio test (LRT) statistic. In general, the former does not yield good power in detecting the signal, and the latter has lacked an analytically tractable reference distribution. Pilla and Loader have introduced a new test statistic based on perturbation theory to detect the presence of a signal. In this talk, we review its reference distribution and note the connection with the LRT. We also illustrate the technique in the context of a model problem from particle physics: the search for a new particle resonance. Monte Carlo results demonstrate the proposed score test is significantly more powerful, resulting in a higher rate of signal detection when a signal is present in the data.