Transcript Diapositive 1

I’ll not discuss about Bayesian or Frequentist foundation
(discussed by previous speakers)
I’ll try to discuss some facts and my point of view.
I think that we cannot solve here a century old debate..
When we do a phenomenological work we should not forget physics
A phenomenological work implies
- to do predictions
- to indicate which are the important things to do/ to measure/ to calculate
- to use all the available informations.
We should keep in mind that with the two approaches we are
answering two different questions (see previous talks).
This statement simply translates into the fact that Bayesians
give PDF and Frequentists give CL.
caveat for Bayesian is the prior dependence.
Caveat for the Frequentist is how to define CL (5%,32%) and
how to treat systematic (often with a bayesian approach) and
of theoretical errors which often have been already combined
SM predictions of Dms
Our collaboration or protocollaboration is in read
(CKMFitter in this figure is in blue)
SM predictions of sin2b
Our collaboration is in read or protocoll. is in blue
(CKMfitter in this figure is in yellow)
sin2b and Dms were predicted before these mesurements.
Crucial test of the SM
Important motivation to perform this measurement
Priors are not a problem. They are part of the Bayesian approach.
We check that any time. If the measurement (likelihood) is starting to be precise,
there is no dependence. In this case the two methods give similar answers.
In other case the question is different the answer is different.
Past comparison Freq/Bayes
Example of depence on prior even in
presence of not very precise (30%)
measurement (g from Dalitz technique)
using Cartesian or Polar coordinates
Frequentist/ Bayesian
Test done with same inputs in 2002
for the first CKM workshop
In the today situation the two
approaches would given even
more similar results
g  (76.7  24.7)
g  (77.0  21.7)
Statistics should not allow people to…forget physics. Example on a
hep-ph/0607246
Our analysis of a was criticised..and not very kindly..because of some argument like
the prior dependence, the dependence of the result from different parametrization +
the fact that we were not able to reproduce the 8 ambiguities…+ the fact that we do
not have a solution at a~0
Recall :
Utfit answer
Please have a look at hep-ph/0701204
submitted to PRD
How it is possible ?
Gronau London method requires some a priori MINIMAL ASSUPTION on
strong interactions, namely
- flavour blindness and CP conservation
- negligible isospin symm. breaking.
We believe that the strong coupling constant has a natural size of LQCD~1GeV
QCD
We do not expect :
1-CL
Frequentist plot from CKMFitter ??
a
In addition.. the Baysian result does not depend on use of different parametrizations
and does not depend on priors (cut on the upper value of |P|) as claimed..
More details on the anaysis of a from M. Bona
presentation at SLAC
Some very instructive slides from a seminar given
by R. Faccini
• The frequentistic approach returns the region of the
parameters for which the data have at least a given
probability (1-C.L.) of being described by the model
– P(data |  ,  region )  1  C.L.
– The true value is a fixed number – no distribution
– Utilize toy MC
CKMFitter (RFit option) http://www.slac.stanford.edu/xorg/ckmfitter
• The bayesian approach tries to calculate the probability
distribution of the true parameters by assigning
probability density functions to all unknown parameters
– Utilize Bayes theorem
– The true value has a distribution
P(data | H ) P( H )
P( H | data) 
– P(H) : a-priori probability
P(data | H ) P( H )dH

UTFit http://www.utfit.org
How to read plots
BABAR
•
1-C.L.
•
a [degrees]
1-C.L.=probability of the data being in worse
agreement than what observed with a given
hypothesis on the true value
The intercepts with 1-C.L.=0.32 are the boundary of
the interval of hypotheses on the true value which are
discarded by the data with a prob. of at least 32%
(the so called “68% C.L. region”).
“Allowed” region
• Prob. Density (“a-posteriori”) is an estimate of the
pdf of the true value
• projection of red area : region by which the true
value is covered at 68% probability
• note that the UTFit convention in case of multiple
peaks is to start from maximum of likelihood and
integrate over equi-probable contours
•Otherwise the integration starts from the median
What they say of each other
P( H | data) 
•
Frequentists of bayesian approach
– A priori probabilities completely arbitrary
P(data | H ) P( H )
 P(data | H ) P( H )dH
– How can I trust a calculation based on something which is completely
unknown?
– Why should I try to calculate something imprecisely if I can already
calculate something exactly? If I can trust the Bayesian result only when
it agrees with the frequentist one, why shall I try it at all !?!
– The integration of the likelihood to get the C.L. regions has degrees of
arbitrariness
•
Bayesians of frequentist approach
– The probability of the true value being in a C.L. region is unknown (not
necessarily above C.L.)
• The result has no really usefulness, in principle the true value could be
anywhere with unknown probability
– There is some freedom in the choice of the test statistics and of the
definition of “worse agreement”.