Limits and confidence intervals in the presence of nuisance parameters

By Wolfgang Rolke, Angel Lopez, Janice Conrad. 2004

617 citations recorded by the source corpus.

We study the frequentist properties of confidence intervals computed by the method known to statisticians as the Profile Likelihood. It is seen that the coverage of these intervals is surprisingly good over a wide range of possible parameter values for important classes of problems, in particular whenever there are additional nuisance parameters with statistical or systematic errors. Programs are available for calculating these intervals.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/0dfe066285b342acd898ecc177935cafcb755003

How researchers see this paper

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

In Finance

In Statistics and Probability

Citations in the corpus

Limits to dark matter annihilation cross-section from a combined analysis of MAGIC and Fermi-LAT observations of dwarf satellite galaxies (2016, positive): “One possible prescription to deal with these cases is to restrict −2 lnλP (〈σv〉 |D) to 〈σv〉 ≥ 0 [56].”
VHE γ-Ray Observation of the Crab Nebula and its Pulsar with the MAGIC Telescope (2007, methodology): “Having defined the signal and background regions in this way, the upper limit on the number of excess events was obtained by the method of Rolke et al. (2005), assuming a systematic uncertainty of 30% on the collection area.”
Limiting two-Higgs-doublet models (2014, background): “7% confidence intervals (χ(2)EW,min is the absolute minimum of χ 2 EW(MA,∆M)) [16, 46].”
Evaluation of three methods for calculating statistical significance when incorporating a systematic uncertainty into a test of the background-only hypothesis for a Poisson process (2007, neutral): “Kf Email addresses: cousins@physics.ucla.edu (Robert D. Cousins), Preprint submitted to Elsevier 31 March 2022”
Dark matter direct-detection experiments (2015, neutral): “worth mentioning that other methods exist which include systematic uncertainties in the confidence interval construction [210][211].”
Dark matter and fundamental physics with the Cherenkov Telescope Array (2012, methodology): “In case of non detection within a certain observation time, we calculate integral upper limits following the methods described in [58] (bounded profile likelihood ratio statistic with Gaussian background, and with a confidence level of 95% C.”
An updated analysis of Inert Higgs Doublet Model in light of the recent results from LUX, PLANCK, AMS-02 and LHC (2013, methodology): “In the next two sections, we will present our results mainly based on “Profile Likelihood” method [148].”
Observation of an anomalous positron abundance in the cosmic radiation (2008, methodology): “The calculation of the confidence interval is based on the likelihood ratio test[45], by considering proper probability models for the positron signal, the proton background, the selection efficiency and the weight w.”