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Bayesian Approach for Sensitivity Estimation in Data Analysis

This study outlines a Bayesian approach for estimating sensitivity in data analysis, focusing on background events, toy Monte Carlo studies, and fitting regions. The approach involves temporary PDFs for signal, radiative, and accidental events, with strategies for estimating their numbers. The study also discusses the estimation of UL on 2008 data.

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Bayesian Approach for Sensitivity Estimation in Data Analysis

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  1. Estimate of Sensitivity with a Bayesian approach G.Cavoto, F.Renga, G.Piredda, C.Voena

  2. Outline • Usetemporarypdfs • Estimate of number of bkgeventsfrom data • Toy MC study and sensitivitystudywithBayesianapproach • FitRegion: +-6sigma: • Eg=44.2-61.4MeV • Ep=48.-57.6 MeV • theg=170-180 degrees • Teg= 24.7-27.1 ns • (Assumedresolutions: • (Ep)=0.8MeV(Eg)=1.43MeV(Teg)=0.2ns, (theg)=30mrad)

  3. Temporary PDFs • SIGNAL • Eg: from full signal MC • Ep: 3-gaussianfromfrancesco’s fit on data • theg: fromtoy MC generation using MC angularresolution • Teg=gaussianwith 0.180 ns (from UL) • RADIATIVE • Ep,Eg,theg: toy MC thatsmear and weightkuno-okada • distributiontakinginto account resolution and acceptance • Teg: gaussianwithsameresolutionassignal • ACCIDENTAL • Eg: fromfittoTegsideband • Ep: fromfrancesco’s fit • theg:fromfittoTegsideband • Teg: flat

  4. Estimate of number of Accidental events • Strategy: • - Countevents in Tegleftsideband (othervariabiles in fitregion) and scale in Tegfitregionassumingflatbkgdistribution • NB=+- • Strategy2: • - FittoEgsidebandwithaccidental+radiativepdf, scale • toEgfitregionusingpdfshape • (thisgivesalso the number of radiativeevents) • NB= • NRD=

  5. Fit to Eg sideband Nacc=zzzz NRD=zzzz

  6. Toy MC results • Non Gaussian • errors with 0 • (low) number of • signal/radiative • events • Need to use • Likelihood to • estimate UL Fitted NS

  7. A Toy MC experiment with high statistics

  8. bayesian UL • On fitted data: • - build a posteriori pdf of BR byweighting the a-priori BR pdf • (flatfrom zero toBRmax) withweight w: • w = exp(-(LogL(NS)-MinLogL)) • where NS for a given BR iscomputedusing the normalization • factor (takinginto account its error) • Estimate of sensitivity • - perform the previousexcercisefor a set of toyswhere Nsgen=0 • We can usethistooltoperformsystematicstudies • Implementationongoing

  9. Estimate of UL on 2008 data Inputs

  10. Conclusion

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