Download Use as variable

MEM Statistics
Jorgen D’Hondt
I was asked to entertain this discussion session
My interpretation: quick overview of some key
issues, and stimulate discussion
MEM workshop – CP3 – May 2013
MEM Statistics
Jorgen D’Hondt
The master formula from theory to experiment
pheno
theory
experiment
http://w3.iihe.ac.be/~jdhondt/Lecture-TheoryVsExp-DHondt-Natal2012.pdf
MEM workshop – CP3 – May 2013
Event-by-event analysis
Jorgen D’Hondt
The MEM master formula (at least a sketch, simplified notation):
for each event
Including nuisance parameters (alpha) :
Using the MEM output
Jorgen D’Hondt
The MEM master formula (at least a sketch, simplified notation):
for each event
Using the MEM output
Jorgen D’Hondt
The MEM master formula (at least a sketch, simplified notation):
for each event
Absolute “likelihood” to construct an estimator
Relative “likelihood ratio” to compare (a possible) Signal to Background
eg. Neyman-Pearson variable
Using the MEM output
Jorgen D’Hondt
The MEM master formula (at least a sketch, simplified notation):
for each event
Absolute “likelihood” to construct an estimator
Relative “likelihood ratio” to compare (a possible) Signal to Background
eg. Neyman-Pearson variable
Using the MEM output
Jorgen D’Hondt
The MEM master formula (at least a sketch, simplified notation):
for each event
Absolute “likelihood” to construct an estimator
Typically SM
measurements
Relative “likelihood ratio” to compare (a possible) Signal to Background
Typically BSM searches
eg. Neyman-Pearson variable
Using the MEM output
Jorgen D’Hondt
The MEM master formula (at least a sketch, simplified notation):
for each event
Absolute “likelihood” to construct an estimator
Use as probability !!
Relative “likelihood ratio” to compare (a possible) Signal to Background
Use as variable !!
eg. Neyman-Pearson variable
Using the MEM output
Jorgen D’Hondt
The MEM master formula (at least a sketch, simplified notation):
for each event
Absolute “likelihood” to construct an estimator
Use as probability !!
Relative “likelihood ratio” to compare (a possible) Signal to Background
Use as variable !!
Footnote: uncorrelated variables PS and PB
eg. Neyman-Pearson variable
Using the MEM output
Jorgen D’Hondt
Absolute “likelihood” to construct an estimator
•
•
•
•
Aim: optimal estimator (closer to the Minimum Variance Bound)
Need simulation to calibrate P(q) to a consistent L(q) probability
The rescaling factor C is very important
Everything can be absorbed in a “black-box” pull correction
Relative “likelihood ratio” to compare S & B
•
•
•
•
Use as probability !!
Use as variable !!
Aim: optimize discrimination power between Signal and Background
Need simulation for a template of the “likelihood ratio” variable
The rescaling factor C is not important
The pull is not important
Using the MEM output
Jorgen D’Hondt
Absolute “likelihood” to construct an estimator
•
•
•
•
Use as probability !!
Aim: optimal estimator (closer to the Minimum Variance Bound)
Need simulation to calibrate P(q) to a consistent L(q) probability
The rescaling factor C is very important
Everything can be absorbed in a “black-box” pull correction
Controlling the statistical properties is very important !
Relative “likelihood ratio” to compare S & B
•
•
•
•
Use as variable !!
Aim: optimize discrimination power between Signal and Background
Need simulation for a template of the “likelihood ratio” variable
The rescaling factor C is not important
The pull is not important
Controlling the statistical properties is less important !
Key feature of MEM
Jorgen D’Hondt
Key feature of MEM
Jorgen D’Hondt
Hence we (always) simplify !
Key feature of MEM
Jorgen D’Hondt
Hence we (always) simplify !
① Absolute: P ≠ probability
② Relative: P = less optimal variable
Key feature of MEM
Jorgen D’Hondt
Hence we (always) simplify !
① Absolute: P ≠ probability
Calibrate using your best knowledge
with data or simulation, or normalize to
P(aSM)
② Relative: P = less optimal variable
Check how much less sensitive you
become to differentiate Signal &
Background
Key feature of MEM
Jorgen D’Hondt
Hence we (always) simplify !
① Absolute: P ≠ probability
Calibrate using your best knowledge
with data or simulation, or normalize to
P(aSM) … eg. which path to follow ?
② Relative: P = less optimal variable
Check how much less sensitive you
become to differentiate Signal &
Background … eg. how to recover
sensitivity of radiation ?
General Wtb vertex physics
Jorgen D’Hondt
• Flavour physics is a key domain and challenge in HEP
• Understanding the mass and mixing patterns is an open issue and relates to
fundamental aspects like CP-violation
• Deviations from the SM expectation in flavour changing processes would be
an important discovery of new physics; new interactions at higher energies
may manifest themselves as effective couplings of the SM fermions
• The W-t-b vertex is an excellent study case for this research
Vtb ~ 1
(SM)
0
(SM)
these “form factors” have complex phases  8 degrees of freedom !
eg. VL,R = Re(VL,R).eif(VL,R)
if CP is conserved the couplings can be taken as real ( 4 degrees of freedom)