CLs method

CLs method
Name	CLs method
Field	Statistics, Particle Physics
Introduced	1990s
Applications	Hypothesis testing, Confidence limits, Exclusion limits

CLs method

The CLs method is a statistical technique used to set exclusion limits in searches for new phenomena in experimental physics, particularly high-energy particle physics. It modifies classical hypothesis testing to reduce the chance of excluding models when sensitivity is low, and has been adopted by collaborations working at facilities such as CERN, Fermilab, and DESY. The approach is frequently employed in analyses by experiments like ATLAS (experiment), CMS (experiment), and LHCb.

Introduction

The method originated during the 1990s in the context of searches for rare signals at facilities including LEP and Tevatron (collider), where teams from collaborations such as ALEPH (experiment), CDF (detector), and DØ (detector) confronted the problem of setting robust limits with low sensitivity. CLs is cited in publications associated with awards and institutions like the Royal Society and technical reports from SLAC National Accelerator Laboratory. It balances control of Type I and Type II error considerations in a way that proved pragmatic for large collaborations at experiments such as BaBar and Belle (particle detector).

Definition and Rationale

CLs defines a modified p-value ratio to decide exclusion. The quantity combines the p-value under the signal-plus-background hypothesis and the p-value under the background-only hypothesis to produce a conservative test statistic. The rationale echoes guiding principles used by committees at organizations like the Particle Data Group and working groups convened by entities such as European Organization for Nuclear Research panels; it aims to avoid excluding models when the experiment lacks power, a concern also debated in panels involving National Academies and review boards tied to projects like ITER.

Statistical Formalism

Formally, let p_s+b denote the tail probability of observing data as extreme or more under the signal-plus-background hypothesis and p_b denote the analogous tail probability under the background-only hypothesis. CLs is defined as CLs = p_s+b / p_b. Exclusion at confidence level α is declared when CLs < α. This construction relates to likelihood-ratio tests introduced by statisticians associated with institutions such as Princeton University, University of Cambridge, and Harvard University and complements approaches like the Neyman construction used in analyses connected to laboratories like Brookhaven National Laboratory and Lawrence Berkeley National Laboratory. The method often employs test statistics derived from profile likelihoods and asymptotic formulae developed by researchers from centers including Imperial College London and University of Oxford.

Implementation and Practical Use

In practice, experiments implement CLs with Monte Carlo techniques and asymptotic approximations incorporated into software frameworks maintained by collaborations such as ROOT (software), RooFit, and tools developed at CERN and Fermilab. Analysts construct toy experiments or use asymptotic distributions to estimate p_s+b and p_b, profiling nuisance parameters tied to systematic uncertainties characterized by groups at institutions like CERN and DESY. Experimental papers from ATLAS (experiment) and CMS (experiment) routinely report CLs-based upper limits on cross sections or coupling parameters, often in combination with constraints from prior results by experiments such as LEP and Tevatron (collider).

Comparisons with Other Methods

CLs is frequently compared to traditional frequentist confidence intervals, the Feldman–Cousins construction, and Bayesian credible intervals. The Feldman–Cousins method, associated with researchers at institutions like University of Rochester and University of Chicago, seeks unified intervals to avoid flip-flopping, while Bayesian methods used by groups at places like Caltech and MIT require priors. CLs tends to be more conservative than pure frequentist tests in low-sensitivity regimes and differs from likelihood-ratio based hypothesis testing practiced in searches reported by collaborations including CDF (detector) and DØ (detector).

Applications in Particle Physics

CLs has been central to exclusion claims in searches for phenomena such as Higgs boson channels investigated at LEP and later at LHC, supersymmetric particles sought by ATLAS (experiment) and CMS (experiment), and exotic resonances probed at Tevatron (collider). It has been used to present limits on parameters in models developed at institutions like CERN theoretical groups and proposals from researchers at Harvard University and Princeton University. Major publications adopting CLs include conference notes and journal articles from collaborations such as ALEPH (experiment), ATLAS (experiment), CMS (experiment), and experiments at DESY.

Limitations and Criticisms

Critics—some from academic departments like University of California, Berkeley and Columbia University and statistical groups associated with laboratories such as SLAC National Accelerator Laboratory—note that CLs is not a standard frequentist confidence level and can be seen as ad hoc. Debates involving committees at organizations like the International Committee for Future Accelerators highlight that CLs may bias reporting toward conservatism and complicate comparisons with Bayesian results reported by groups at places like Stanford University and Yale University. The method's dependence on choice of test statistic, treatment of nuisance parameters, and computational approximations has motivated alternative proposals in the literature from authors affiliated with institutions including CERN, University of Oxford, and Imperial College London.

Category:Statistical methods