Hello all,

In IntervelCalculator, there must be a model, a data set, a set of parameters of interest, a set of nuisance parameters and a confidence level.

My question is,
(1)how to get the confidence interval and the best fit parameter of interest(i.e.the mean value)according to some pdf without a data set. Because the data set is generated by ourselves and the result we get by using a data set does not have general statistical significance.
(2)how to get the standard deviation in the profile likelihood ratio, by which we can also obtain the error band of the upper/lower limit.
Hope for any help from you.

thanks & regards,
Hanyu

Hi,

I am not sure I have understood your question, but the ProfileLikelihoodCalculator (PLC) finds the interval
(upper/lower limit) or just upper (lower) limit if the parameter is bounded on the lower (upper) side.
The interval is obtained from the likelihood which is built on a given data set. So you always need a data set for finding the interval.
The observed interval will be obtained using the observed data set. If you want an expected interval, you can find it by averaging the result on all the possible data sets you can generate using the given model.
The limit bands can be obtained then from the distributions obtained on the interval limits.

To get a limit and bands using a likelihood based method, you might want to look also at the AsymptoticCalculator class, which used in combination with the HypoTestInverter performs an interval calculation using the asymptotic formula for the profile likelihood.
Using these class you can get also the bands for your limits, using an Asimov data set.
See the roostats macro, StandardHypoTestInvDemo, run with the option =2 for the calculator type
root.cern.ch/root/html/tutorials … emo.C.html

Best Regards

Lorenzo

Thanks a lot.

Hanyu