Up: Inferring the success parameter
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The classical inverse problem related to the binomial distribution
has been reviewed and extended to the presence of background
either only on the number of `successes', or on the trials
themselves. The probabilistic approach followed here allows
to treat the problems only using probability rules.
The results are always in qualitative agreement with
intuition, are consistent with observations and prior knowledge
and, never lead to absurdities, like outside the range
0 and 1.
The role of the priors, that are crucial to allow the
probabilistic inversion and very useful to balance in the
proper way prior knowledge and evidence from new observations,
has been also emphasized, showing when they can be neglected
and when they are so critical that it is preferable not
to provide probabilistic conclusions.
It is a pleasure to thank Stefano Andreon for several
stimulating discussions on the subject.