Limits and Confidence Intervals in the Presence of Nuisance Parameters

Rolke, Wolfgang; López, A.; Conrad, J.

doi:10.1142/9781860948985_0021

Cited by 55 publications

(72 citation statements)

References 14 publications

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“…A eff (E ′ ; ∆E) is the effective area for events with measured energy within ∆E, as a function of true energy E ′ ; N UL ex is computed using global N ON , N OFF and τ values and the conventional method [37], for a 95% CL and assuming a systematic uncertainty on the overall detection efficiency of 30%. A eff (E ′ ; ∆E) is computed for the entire sample as the weighted average of the effective areas of the four considered data sets, with weights being the corresponding observation times, i.e.…”

Section: Discussionmentioning

confidence: 99%

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Optimized Dark Matter Searches in Deep Observations of Segue 1 with MAGIC

Aleksić

2016

Springer Theses

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Abstract. We present the results of stereoscopic observations of the satellite galaxy Segue 1 with the MAGIC Telescopes, carried out between 2011 and 2013. With almost 160 hours of good-quality data, this is the deepest observational campaign on any dwarf galaxy performed so far in the very high energy range of the electromagnetic spectrum. We search this large data sample for signals of dark matter particles in the mass range between 100 GeV and 20 TeV. For this we use the full likelihood analysis method, which provides optimal sensitivity to characteristic gamma-ray spectral features, like those expected from dark matter annihilation or decay. In particular, we focus our search on gamma-rays produced from different final state Standard Model particles, annihilation with internal bremsstrahlung, monochromatic lines and box-shaped signals. Our results represent the most stringent constraints to the annihilation cross-section or decay lifetime obtained from observations of satellite galaxies, for masses above few hundred GeV. In particular, our strongest limit (95% confidence level) corresponds to a ∼500 GeV dark matter particle annihilating into τ + τ − , and is of order σ ann v ≃ 1.2×10 −24 cm 3 s −1 -a factor ∼40 above the σ ann v thermal value.

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Section: Discussionmentioning

confidence: 99%

“…We note that the results obtained this way are conservative (i.e. they may have a slight over-coverage, see [37]), since negative fluctuations cannot produce artificially constraining limits.…”

Section: Full Likelihood Analysismentioning

confidence: 97%

Optimized Dark Matter Searches in Deep Observations of Segue 1 with MAGIC

Aleksić

2016

Springer Theses

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“…While there are possible ways to incorporate systematic uncertainties without leaving the frequentist framework (see, for example, [104]), there are some potential drawbacks with these solutions. After comparing the characteristics of a few options (see Section 8.3.3), we decided to use a semi-Bayesian technique to incorporate systematic errors.…”

Section: Systematic Error Incorporationmentioning

confidence: 99%

Indication of Electron Neutrino Appearance from an Accelerator-Produced Off-Axis Muon Neutrino Beam

Abe¹,

Abgrall²,

Ajima³

et al. 2011

Phys. Rev. Lett.

1,205

627

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T2K (Tokai to Kamioka) is a long baseline neutrino experiment with the primary goal of measuring the neutrino mixing angle θ 13 . It uses a muon neutrino beam, produced at the J-PARC accelerator facility in Tokai, sent through a near detector complex on its way to the far detector, Super-Kamiokande. Appearance of electron neutrinos at the far detector due to oscillation is used to measure the value of θ 13 .

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“…To compare this Bayesian method with the frequentist approach, we have also determined the 90% upper limit for the source rate using the Feldman-Cousins [9] and Rolke et al [10] We see that the Bayesian approach is equal to the Rolke et al method and is more conservative than the Feldman-Cousins method. To further test the upper limit calculation, we have generated source signals (or under-fluctuations) by increasing (or decreasing) the number of events in the on-source region, while keeping the same number of background events as in the data.…”

Section: Determination Of the Source Ratementioning

confidence: 99%

“…In the light of a flux upper limit determination we will discuss a method following the Bayesian framework and a comparison will be made to the standard frequentist methods developed by Feldman and Cousins [9] and Rolke et al [10]. The Feldman-Cousins method introduces the likelihood ratio as an ordering principle, when determining the acceptance interval from which one derives the confidence interval.…”

Section: Introductionmentioning

confidence: 99%

Bayesian approach for counting experiment statistics applied to a neutrino point source analysis

Bose

Brayeur

Casier

et al. 2013

Astroparticle Physics

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In this paper we present a model independent analysis method following Bayesian statistics to analyse data from a generic counting experiment and apply it to the search for neutrinos from point sources. We discuss a test statistic defined following a Bayesian framework that will be used in the search for a signal. In case no signal is found, we derive an upper limit without the introduction of approximations. The Bayesian approach allows us to obtain the full probability density function for both the background and the signal rate. As such, we have direct access to any signal upper limit. The upper limit derivation directly compares with a frequentist approach and is robust in the case of low-counting observations. Furthermore, it allows also to account for previous upper limits obtained by other analyses via the concept of prior information without the need of the ad hoc application of trial factors. To investigate the validity of the presented Bayesian approach, we have applied this method to the public IceCube 40-string configuration data for 10 nearby blazars and we have obtained a flux upper limit, which is in agreement with the upper limits determined via a frequentist approach. Furthermore, the upper limit obtained compares well with the previously published result of IceCube, using the same data set.

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Limits and Confidence Intervals in the Presence of Nuisance Parameters

Cited by 55 publications

References 14 publications

Optimized Dark Matter Searches in Deep Observations of Segue 1 with MAGIC

Optimized Dark Matter Searches in Deep Observations of Segue 1 with MAGIC

Indication of Electron Neutrino Appearance from an Accelerator-Produced Off-Axis Muon Neutrino Beam

Bayesian approach for counting experiment statistics applied to a neutrino point source analysis

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