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Non-gaussian statistics Location and scale An easy application

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Presentation on theme: "Non-gaussian statistics Location and scale An easy application"— Presentation transcript:

1 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

2 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!

3 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:

4 Functions 1 Gauß: Median: „Paw“:

5 Functions 2 Huber: Tukey: Hampel:

6 Location and Scale Results: The robust guys do much better!
BUT: It is your choice for parameters!

7 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!

8 Application 1.1 1. Fight against the combinatorics

9 Application 1.2 2. nice results, but we need a guess!

10 Application 1.3 3. Line-guesses

11 Application 1.4 3. Line-guesses (cont.) 4. Estimating the scale:
=> The robust-statistics has its limits!!

12 Application 1.5 5. Lets fit: (Minimising, using )
REGRESSION with distance to 0 and angle!

13 Application 1.6 REGRESSION (cont.): Hampel (bad scale) sine-function:

14 Application 1.7 6. Line fit, hampel:

15 Application, results 1 7. Final:

16 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!

17 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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