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Results may be combined in a natural way
making an interactive use of
Bayesian inference.
As a first case we assume
several experiments having the same efficiency and exposure time.
 Prior knowledge:
 Experiment 1 provides Data:
 Experiment 2 provides Data:
 Combining similar independent experiments we get
Then it is possible to evaluate expected value, standard deviation,
and probability intervals.
As an exercise, let us analyse the two extreme cases, starting
from a uniform prior:

 if none of the similar
experiments has observed events
we have
expts evts 



expts evts 





with probability 


 If the number of observed events is large (and the prior flat),
the result will be normally distributed:
Then, in this case it is more practical to use maximum likelihood
methods than to make integrals (see Section ).
From the maximum of
, in correspondence of
,
we easily get:
E
and from the second derivative of
around the maximum:
Next: Combination of results: general
Up: Poisson model: dependence on
Previous: Dependence on priors
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Giulio D'Agostini
20030515