Unfolding algorithms and RooUnfold
Prof. dr hab. Elżbieta Richter-Wąs
Unfolding algorithms:
Extracted from slides by T. Adye at PHYSTAT 2016 and K.
Reygers lectures at Heilderbeg Univ.
S. Smitt and D. Britzger, DESY Stat School 2014
S. Schmitt , QCDHS conference in 2016
Unfolding
2
What is unfolding
3
ATLAS analysis example
4
Migrations and stat. fluctuations
5
Formal definitions
6
Unfolding methods
7
„Bin-by-bin”
8
Bin-by-bin correction factors
9
Simple „Bin-by-bin”: why is it wrong?
10
Matrix methods
11
Matrix inversion
12
Cause of large fluctuations
13
Template fit
14
Template fit with area constraint
15
Tikhonov regularisation
16
Tikhonov regularisation (eg. TUnfold)
17
Iterative method
18
Iterative method with background
19
Evaluation of the coveriance matrix
20
Iterative method: Oth iteration
21
Iterative method: 1st iteration
22
Iterative method: 10th iteration
23
Iterative method: 100th iteration
24
Iterative method: 1000th iteration
25
Over- and Under-Regularised Unfolding
26
Selection of other unfolding methods
27
RooUnfold package
28
RooUnfold features
29
RooUnfold testing
30
RooUnfold classes
31
RooUnfold example (Bayes)
32
RooUnfold example (Bayes)
33
RooUnfold algorithms: Iterative Bayes
34
RooUnfold algorithms: SVD
35
RooUnfold algorithms: TUnfold
36
RooUnfold algorithms: Unregularised
37
RooUnfold algorithms: comparison
38
RooUnfold with Bayes algorithm (3 iterations)
39
RooUnfold with SVD algorithm ( k=30 )
40
RooUnfold with TUnfold algorithm ( t=0.004 )
41
Unregularised matrix inversion
42
Simple correction factors
43
Unfolding errors
44
Bin-to-bin correlations
45
Which Method To Choose?
46
Summary
47
References
48
49
Deconvolution
50
To Unfold or Not?
51
When Unfolding Make Sense
52
When Unfolding Make Sense
53
Response Matrix (I)
54
Response Matrix (II)
55
Response Matrix (III)
56
Response Matrix (IV)
57
Unfolding by Inverting Responce Matrix (I)
58
Unfolding by Inverting Responce Matrix (II)
59
Unfolding by Inverting Responce Matrix (III)
60
What’s Wrong with the Matrix Inversion Method?
61
Bin-by-Bin Method (I)
62
Bin-by-Bin Method (II)
63
Regularized Unfolding
64
Tikhonov Regularization
65
