ms limit: the Likelihood
- Likelihood = L( ms , gi )
- ms = only free parameter
- gi = “external” (fixed) parameters ( fs , fd, md, , bckg., )
- (Log) Likelihood difference:
DLL= ln(L( ms )) - ln(Lmin)
- 95 % lower limit :
intersection of DLL
with 95 % C.L. curve
- Ideal (symmetric ) case :
- Fast MC. For several ms values :
- generate (~1000) samples with same statistics as the data
- in each sample vary gi within errors (include systematics)
- find value of ln(L) below which lie 95 % of the sample
How to combine limits ?