Reminders from lecture 1 and 2
Expected results and toys
Pseudo-experimens and Asimov datasets
Dealing with non-asymptotic situations
Profiling
Look-Elsewhere Effect
Bayesian method
Presentation of results
Statistics and Data Analysis (HEP at LHC)
Prof. dr hab. Elżbieta Richter-Wąs
Slides extracted from N. Berger lectures at CERN Summer School 2019
Reminders from Lecture 1: Statistical Model
2
Reminders from Lecture 1: Statistical Model
3
Model Parameters
4
Model Example
5
Statistical Results as Hypothesis Tests
6
Test Statistics for Discovery
7
Discovery p-value
8
Reminder: Wilk’s Theorem
9
Asymptotic Approximation
10
Discovery significance
11
Takeaways: Discovery Significance
12
Hypothesis testing: One-Sided vs Two-Sided
13
One-Sided Asymptotics
14
Test Statistic for Limit-Setting
15
Takeaways: Limits & Intervals
16
Generating Pseudo-data
17
Expected results
18
Expected limits: Toys
19
CLS: Gaussian Bands
20
Expected limits: Asimov Datasets
21
Beyond Asymptotics: Toys
22
Toys: Example
23
Remarks
24
Nuisances and Systematics
25
Likelihood, the full version (binned case)
26
Frequentist Constraints
27
Wilks’ Theorem
28
Systematics implementation
29
Gausian Profiling
30
Profiling example
31
Uncertainty decomposition
32
Pull/Impact plots
33
Pull/Impact plots
34
Takeaways
35
Summary on Statistical Results Computation
36
Look-Elsewhere effect
37
Global Significance
38
Global Significance from Toys
39
Global Significance from Asymptotics
40
Global Significance from Asymptotics
41
Illustrative Example (1)
42
Illustrative Example (2)
43
Illustrative Example (3)
44
ZGlobal Asymptotics Extrapolation
45
Trials factor
46
Frequentist vs. Bayesian
47
Frequentist vs. Bayesian
48
Bayesian methods
49
Frequentists method: CLS computation
50
Bayesian method: Bayesian limit
51
Bayesian methods
52
Why 5s?
53
Reparametrisation
54
Reparametrisation: Limits
55
Presentation of results
56
Conclusions
57
