A Combining separate upper & lower limits into a total?

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Combining upper and lower limits from two separate experiments is not valid by simply summing the individual upper limits, as this would yield a weaker limit. Correlations and systematic errors between the experiments must be considered for a proper analysis. If the data comes from a single Monte Carlo simulation, the situation becomes more complex due to inherent correlations. Understanding the systematic errors is crucial for accurate results. Overall, additional information is necessary to make valid conclusions about combined limits.
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If the results of two separate experiments to measure the same quantity are stated in terms of upper and lower limits at the same confidence level, is it valid to say that the overall upper limit (at the same C.L.) is just the sum of the two individual upper limits? Or is something more complicated necessary here?
 
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Anchovy said:
is it valid to say that the overall upper limit (at the same C.L.) is just the sum of the two individual upper limits?
No, definitely not. That would be a weaker limit with more data!

In general, there might also be correlations and systematics that are the same in both experiments. You need to have more information to do a proper analysis.
 
Orodruin said:
No, definitely not. That would be a weaker limit with more data!

In general, there might also be correlations and systematics that are the same in both experiments. You need to have more information to do a proper analysis.

Ah, I see. Do things become much simpler if it's not actually two different experiments, but rather it's one Monte Carlo simulation, counting the same thing happening two different ways?
 
You would still need to know a lot more about the actual simulation in order to make a statement. In particular about the systematic errors going in.
 
Orodruin said:
You would still need to know a lot more about the actual simulation in order to make a statement. In particular about the systematic errors going in.

OK, thanks.
 
I think just addining them will result to taking them 100% correlated, in contrast to adding them in quadrature... but as already pointed out, without knowing information on systematics, it will not give you the right result...
 
Anchovy said:
Ah, I see. Do things become much simpler if it's not actually two different experiments, but rather it's one Monte Carlo simulation, counting the same thing happening two different ways?
That probably makes it more complicated, as the two values are now certainly correlated.
 

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