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Let us
state Bayes' theorem in terms of several independent
causes (
) which
can produce one effect ().
For example, if we consider deepinelastic scattering events,
the effect can be the observation of
an event in a cell of the measured quantities
.
The causes are then all the possible cells of the true values
.
Let us assume we know the
initial probability of the causes and the conditional
probability that the th cause will produce the effect
.
The Bayes formula is then

(7.1) 
depends on the initial
probability of the causes.
If one has no better prejudice
concerning
the process of inference can be started
from a uniform distribution.
The final distribution depends also on
. These probabilities must
be calculated or estimated with Monte Carlo methods. One
has to keep in mind
that, in contrast to , these probabilities are not updated
by the observations. So if there are ambiguities
concerning the choice of
one has to try
them all in order to evaluate
their systematic effects on the results.
Next: Unfolding an experimental distribution
Up: Bayesian unfolding
Previous: Problem and typical solutions
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Giulio D'Agostini
20030515