Finding an Upper Limit in the Presence of Unknown Background

By S. Yellin. 2002

273 citations recorded by the source corpus.

Experimenters report an upper limit if the signal they are trying to detect is non-existent or below their experiment's sensitivity. Such experiments may be contaminated with a background too poorly understood to subtract. If the background is distributed differently in some parameter from the expected signal, it is possible to take advantage of this difference to get a stronger limit than would be possible if the difference in distribution were ignored. We discuss the ``Maximum Gap'' method, which finds the best gap between events for setting an upper limit, and generalize to ``Optimum Interval'' methods, which use intervals with especially few events. These methods, which apply to the case of relatively small backgrounds, do not use binning, are relatively insensitive to cuts on the range of the parameter, are parameter independent (i.e., do not change when a one-one change of variables is made), and provide true, though possibly conservative, classical one-sided confidence intervals.

Subfields: Artificial Intelligence, Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1bb4847de4b899fa0e7fe140025d41f6bf58367d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. P. Madau
2. T. Undagoitia
3. Jure Zupan
4. B. Moore
5. N. Weiner
6. Marcel Zemp
7. Joachim Kopp
8. Michael J. Reece

In Computer Networks and Communications

1. P. Madau
2. T. Undagoitia
3. Jure Zupan
4. B. Moore
5. N. Weiner
6. Marcel Zemp
7. Joachim Kopp
8. Michael J. Reece

In Statistical and Nonlinear Physics

1. L. Strigari
2. P. Madau
3. T. Undagoitia
4. Jure Zupan
5. B. Moore
6. N. Weiner
7. Marcel Zemp
8. Joachim Kopp

Citations in the corpus

• The four basic ways of creating dark matter through a portal (2011, unknown): “To set the limit we have used the Monte-Carlo code for the Optimal Gap Method, provided by Yellin and described in details in [24].”
• Non-relativistic effective theory of dark matter direct detection (2010, methodology): “For CDMS-II, XENON10, and XENON100, we will use the maximum gap method [27] to set limits while for COUPP, we will take the 90% CL Poisson limit from their three DM candidate events, allowing ∼ 6 events.”
• Characterising dark matter searches at colliders and direct detection experiments: vector mediators (2014, unknown): “Our LUX limits (red) are calculated with the ‘pmax’ method, introduced in [94] and the limit on σ0 SI agrees with the published LUX limit to better than 10% over the whole mass range.”
• Dark matter direct-detection experiments (2015, methodology): “If no background prediction is available, possible or its uncertainty is too large, Yellin’s method [215] can be used.”
• A taste of dark matter: flavour constraints on pseudoscalar mediators (2014, unknown): “We follow the analysis strategy described in [121] based on the ‘pmax’ statistic [122] and we have checked that the binned likelihood method from [123] gives very similar results.”
• Dark matter direct detection with non-Maxwellian velocity structure (2009, methodology): “However, many limits are placed using one of Yellin’s techniques [69], where not only the overall rate, but also the distribution of signal versus background is important.”
• Global interpretation of direct Dark Matter searches after CDMS-II results (2009, methodology): “We analyze the XENON data using the maximum gap method [48].”
• Neutrino coherent scattering rates at direct dark matter detectors (2009, background): “Present direct detection experiments report upper limits on the WIMP mass and cross section under the assumption of unknown backgrounds [5].”