Confidence Level Computation for Combining Searches with Small Statistics

Confidence Level Computation for Combining Searches with Small Statistics

February 5, 1999 | Thomas Junk
This article presents an efficient method for computing approximate confidence levels (CL) for combining searches with small statistics, particularly useful in particle physics experiments where the expected signal and background levels are low. The method allows for the combination of results from multiple independent searches, regardless of the discriminating variables measured for candidate events. Systematic uncertainties in the signal and background models are incorporated into the confidence levels. The procedure involves binning the search results in discriminant variables and treating each bin as an independent counting search. The test statistic used is the likelihood ratio, which is the most powerful for distinguishing the signal-plus-background hypothesis from the background-only hypothesis. The confidence levels are calculated using a combination of Poisson probabilities and the cumulative distribution function of the test statistic. The method is validated through numerical examples, including a mock Higgs boson search and the combination of results from multiple LEP experiments. The technique is shown to be accurate and conservative, with adjustable precision. It is particularly useful for scanning a large number of possible models and combining search results sensitive to different signatures.This article presents an efficient method for computing approximate confidence levels (CL) for combining searches with small statistics, particularly useful in particle physics experiments where the expected signal and background levels are low. The method allows for the combination of results from multiple independent searches, regardless of the discriminating variables measured for candidate events. Systematic uncertainties in the signal and background models are incorporated into the confidence levels. The procedure involves binning the search results in discriminant variables and treating each bin as an independent counting search. The test statistic used is the likelihood ratio, which is the most powerful for distinguishing the signal-plus-background hypothesis from the background-only hypothesis. The confidence levels are calculated using a combination of Poisson probabilities and the cumulative distribution function of the test statistic. The method is validated through numerical examples, including a mock Higgs boson search and the combination of results from multiple LEP experiments. The technique is shown to be accurate and conservative, with adjustable precision. It is particularly useful for scanning a large number of possible models and combining search results sensitive to different signatures.
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