I tried roofit with some parameters.
And, for one parameter, par0, I set the limit that par0 > 0, since par0 means number of events of certain background component.
The results of fit is like following.
par0 = 0 +/-39+/-(0,37)
As far as I know, the first error is parabolic error and the second one is minos error.
And, I would like to use minos error, but I am really curious about what is the exact coverage of this error interval since this is estimated at the boundary.
Can I interprete , say, (0,37) as 68% confidence interval ?
since you are at the boundary most probably your coverage will not be correct anymore. You should run toys to verify it. Running something like the RooStats::FeldmanCousins would be more appropriate to get the right frequentist interval in this case
In addition to what Lorenzo said, there is no reason to constrain a background to be positive and good reasons not to (including avoiding the same problem you are having now). When estimating a small background in a fit that is insensitive to that background, you’ll end up with a negative estimate half of the time and that’s o.k. In any case, running PEs (pseudo-experiments) is the minimum you should be dong and a full Feldman-Cousins construction isn’t a bad idea either.
Thanks for kind reply.
In using feldman-cousins limit, what error should I refer to?
At the boundary, I think parabolic error and minos error may be wrong.
Feldman-Cousins is a frequentist interval estimation based on the Neyman construction using the likelihood ratio ordering principle. You can refer to their original paper:
Feldman, G. and Cousins, R. (1998). Unified approach to the classical statistical analysis of small signals. Phys. Rev. D 57 3873-3889.
Otherwise see also some statistics books, like F. James, `Statistical Methods in Experimental Physics, 2nd edition, page 229.