TEfficiency output versus posterior distribution

Newbie
1

Hi all,

I have a question about the TEfficiency class. I am trying to calculate the error given by the division of two efficiencies (data and simulation) and for that I will try to generate random numbers using the posterior pdf of the efficiencies. If I understood correctly the documentation of TEfficiency, when using a uniform prior the posterior is still a Beta distribution with modified a,b parameters: a’=a+k, b’=a+n-k.

The following code shows the efficiency calculation in one bin. The efficiency returned is: 0.0176604693439. However, the function’s integral tells me that the mode is in a higher position (around 0.0183 as shown in the plot). Do you know what might be the cause of this?

roothelp
roothelp.png827×320 10.7 KB

Thanks,
Christos Vergis

    if(ROOT.TEfficiency.CheckConsistency(hpas2,htot2)):
        ef = ROOT.TEfficiency(hpas2, htot2)
        ef.SetPosteriorMode()
        ef.SetStatisticOption(ROOT.TEfficiency.kBUniform)

        n = htot2.GetBinContent(5)    #969.47479248 
        k = hpas2.GetBinContent(5)  #17.1213798523
        apr = ef.GetBetaAlpha(5)+k
        bpr = ef.GetBetaBeta(5)+n-k
        fun = ROOT.TF1("fun","TMath::BetaDist(x,%s,%s)"%(apr,bpr),0,1)
        fun.SetNpx(10000)

        fun.DrawIntegral()
        print ef.GetEfficiency(5),ef.GetEfficiencyErrorLow(5),ef.GetEfficiencyErrorUp(5)
2

Hi,
Sorry I managed to understand my misconception, being that the mode would be the same as the median. Since that is not true, everything is clear.

Thanks.