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?