# Very strange HypoTestInverter scanning curve

Dear experts,

I am using AsymptoticCalculator, I do PoI scanning from 0 to 3, with 300 steps. But if you look the attached HypoTestInverter plot, it seems no any point has been done between 0 and 1, why this can happen ? I didn’t explictly ask and value between 0 to 3 should be skipped …
Please also look the attached workspace: TestWS.root

Many thanks!
Javier
HypoTestInverter_Scan.pdf (48.1 KB)

Hi,

It is strange you don’t have any points between 0,1. Unfortunately I cannot reproduce your result, because if I use your workspace I see that several fits failing. Which version of ROOT are you using?

However I noticed that your best fit results is around 1. If you are using the one-sided test statistics with the asymptotic calculator to compute a limit, by definition all value of q_mu (the one-side profiled log-likelihood ratio) is zero, therefore CL_sb = 0.5.

Best Regards

Lorenzo

Dear Lorenzo,

Many thanks for the reply! I am using v5-34.
"If you are using the one-sided test statistics with the asymptotic calculator to compute a limit, by definition all value of q_mu (the one-side profiled log-likelihood ratio) is zero, therefore CL_sb = 0.5. "
Yes, I am using one-sided. I am a bit confused, would we need to use one-sided or two-sided ? Which one is allowed and can give the correct results ?

Thanks again!
Javier

Dear Lorenzo,

I fixed the failed fittings. And use one-sided. All the ± 1/2 sigma and also the expected curves look reasonable. But the observed CLs curve looks very strange, it is much higher than other lines. But when I draw the data/MC plots, I see the agreement is good. Then why the observed curve is so crazy ? Please see the new workspaces and scanning plot.

Thanks!
Javier
HypoTestInverter_Scan_120.smallRange.1side.root.pdf (34 KB)

Hi,

I still cannot reproduce your results. But the new plot looks reasonable to me. It shows that you have a best fit value of around 0.5.

If the observed is higher than expected this is normal, because you have some signal in the data (best fit value is 0.5) this makes sense. You will get in this case a lower limit.

The one-side test statistics makes sense if you want to estimate a upper limit. In case you want to estimate an interval you can try using the 2-sided test statistics, which is equivalent to a Feldman-Cousins interval, if you are using toys. If not it is an asymptotic approximation of Feldman Cousins.

Lorenzo