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The ``2000 CKM-triangle analysis'' by Ciuchini et al. [1]
is in my opinion the most accurate way
to use consistently all pieces of experimental and theoretical
information relevant to infer, within the
framework of the Standard Model (SM), the parameters of the
unitarity triangle. The basic idea is that
beliefs (i.e. probabilities)
on the value of each *input* quantity are propagated into beliefs
about the *output* quantities, namely and ,
and SM related quantities. The propagation is performed using the rules
of logic applied to uncertain events, i.e. probability theory,
without arbitrariness or ``prescriptions''. All hypotheses are
clearly stated and the influence on the results of
__reasonable__ variations of models and model parameters
have been checked and found irrelevant (see Ref. [1]
for details). Such a propagation of uncertainty, done by
responsible people on physics quantities they feel
knowledgeable about should not be confused with the kind of
mathematical games described in Appendix A of Ref. [2].
In other words, when we say that the value of a quantity
has 50% probability to lie in a certain region, __given__
well defined hypotheses and with reasonably large flexibility of them,
means that we are equally confident that it could be there or elsewhere.
This is in contrast to
``95% C.L. results'' which should not be interpreted
as 95% confidence on a certain
statement (see e.g. Section 5.2 of Ref. [3], and
the Conclusion of Ref. [4] for an independent
account).
The motivation of this note is to illustrate a simplified
way to perform the analysis of Ref. [1]. In fact,
the Monte Carlo integration used there could seem
a bit mysterious.
As well known, approximations usually loose accuracy,
but often help in gaining awareness. And this is exactly the spirit
of this note. Therefore, I have little to add here to
phenomenology, experimental data and inferential framework
of the analysis, and I point
to Ref. [1] and references therein.

The note is organized in the following way.
In Section 2 the relations between
CKM parameters are schematically recalled.
In the following sections
the reweighting effect on the points of the
- plane due to
all pieces of information, is shown in detail.
The final result is then compared to that of Ref. [1].

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Giulio D'Agostini
2004-01-20