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# Bayes' theorem stated in terms of causes and effects

Let us state Bayes' theorem in terms of several independent causes ( ) which can produce one effect (). For example, if we consider deep-inelastic 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   Contents
Giulio D'Agostini 2003-05-15