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## Combination of results from similar experiments

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:

Data   Data

• Combining similar independent experiments we get
 (9.6)

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   Contents
Giulio D'Agostini 2003-05-15