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Bootstrap Methods
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The best one !!!
The non parametricSampling methods
Up to 2006
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Non parametric Bootstrap
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Bootstrap of B1 and Bi data
Trimmed mean 50%Correlation between measurementsWeighted resampling Int(1/s2) timesThe error on measurements is not considered
Scope of the analysis: to test wether errors only or the data itself are unreliable
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Results
Bootstrap:
Standard analysis:
1.36.03.1
3.818.85
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9.33.05.1
6.806.86
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Some data areunreliable
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Useful when the two samples are signal and background....
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The dual Bootstrap
Fix the background on one sample and calculated the peak signalwith another sample to avoid biases !!
Repeat on bootstrap samples (dual bootstrap)
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A word on the permutation tests
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Conclusions•Poissonian Counting: most of the tests do not consider the error on background andoverestimate the signal. Often true (mean) valuesand measured values are improperly confused.
•Binomial counting: a general theory there existsand should be applied.
•The errors should be calculated by MC methodsand the procedure checked with MC toy models
•Nonparametric Bootstrap methods should be usedalso by physicists