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Non-gaussian statistics Location and scale An easy application
M. Bräuer DQ Analysis Motivation Non-gaussian statistics Location and scale An easy application .... A new pre-tracking alignment? Conclusions and plans
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Motivation Physics needs clean and interpretable signals !
=> Gaussian statistics (Lep Higgs-analysis..) We do have noise, bad hardware, process-noise and hadronic dirt One solution: DQ-systems! Example: Searching for bad-VDS-chips Get the deviation from the mean of a group of chips The mean does not work too good! Histogramming and fiting? => even paw gives you a bad day!
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Non-gaussian statistics
There is a vast literature of analysis with heavy-tail-distributions: Outlier „Robust Statistics“ Understanding: Least-Squares: Leads to: Only in the gaussian case ! Otherwise: get rid of the square: Define: Assume:
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Functions 1 Gauß: Median: „Paw“:
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Functions 2 Huber: Tukey: Hampel:
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Location and Scale Results: The robust guys do much better!
BUT: It is your choice for parameters!
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Application 1 Correlations saved not only my but at least once!
Can we look for them automatically? It is an application of fits with robust statistics!
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Application 1.1 1. Fight against the combinatorics
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Application 1.2 2. nice results, but we need a guess!
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Application 1.3 3. Line-guesses
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Application 1.4 3. Line-guesses (cont.) 4. Estimating the scale:
=> The robust-statistics has its limits!!
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Application 1.5 5. Lets fit: (Minimising, using )
REGRESSION with distance to 0 and angle!
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Application 1.6 REGRESSION (cont.): Hampel (bad scale) sine-function:
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Application 1.7 6. Line fit, hampel:
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Application, results 1 7. Final:
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pre-tracking alignment?
A new idea of pre-tracking: The data is processed tracking-free! One can relate the lines to alignment data: => A lot of work still remains, but it looks good!
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Conclusions and outlook
Sometimes the gauss-stuff does NOT hold! Hard to simulate, but data is there in DQ applications Nice results for simple tasks even fitting in high-background data is possible VDS alignment is as LeastSquares one. It had to be robustified to get better results! There are good tools out, why not using them?
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