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Hi Oliver, the way I see it is the following. In the fit w/o categories you are constraining the ratio of the events in each category to be the same as in your MC. In the fit with categories you let these ratios float. The 50 events where artificially created in the fit w/o categories: they were not actually there, but the categories with the biggest errors (the last ones) had to accomodate to satisfy the constraint. This is the same reason why the error increases: we are giving up a set of very powerful constraints, thus paying in the statistical error. hope this helps ciao ric On Mon, 29 Apr 2002, Oliver Buchmueller wrote: > > Ok, so why do you get 559+-44 w/o cat. > and 509+-44 with cat.? > > Or more detailed: > a) What happened to the other 50 events? > b) Why do you get the same error for 509 and 559 events? > > > > > On Mon, 29 Apr 2002, Daniele del Re wrote: > > > > > Hi Oliver, > > > > > Now I am really confused. > > > > > > You are trying to make me believe that the total number of > > > measured events dependence on the categorization. Well, I > > > always thought that adding up the individual cat. should yield > > > the same number of events than making no categorization. > > > Apparently thats not the case ... why? If everything > > > is self consistent it should ... isn't it. > > > At this stage we do not have to care about eff. corrections. > > > > I don't want to make you believe anything, I am just saying that > > > > 1) I calcute how many events I have per category > > 2) I apply the efficiency per category to those numbers > > 3) I put together the numbers > > > > this is different from putting them together before and then dividing by > > the overall efficiency. The final number and the final error > > come out different (as I showed in the simple example in the previous > > mail). > > > > Cheers, > > > > Daniele > > > > > > > > > > > > > > > Oliver > > > > > > By the way, > > > > > > even in your simple example the total number of measured > > > events before eff. correction has to be the same. If you would have > > > a 10% discrepancy there; at least one of the two results (with or w/o > > > cat.) has to be wrong. > > > > > > > > > On Mon, 29 Apr 2002, Daniele del Re wrote: > > > > > > > > > > > Hi, > > > > > > > > > Thanks Daniele, I will think about this eff. stuff a bit more. > > > > > However, in my last mail I was indicating a much more basic item only related to > > > > > the measurement of number of events. Your measurement is: > > > > > > > > > > 559+-44 w/o cat. > > > > > 509+-44 with cat. > > > > > > > > > > => same error but roughly 10% different yield (correct?) > > > > > > > > yes, this 10% less explains the difference but this effect will be > > > > enhanced once you apply the efficiency per category. > > > > You must get the same error if you put together the number before the > > > > efficiency correction. > > > > > > > > > > > > > > Even in your example > > > > > below you assume the same number of measured events ..isn't it. > > > > > This 10% might explain the difference between old and new results. > > > > > > > > > > The eff. stuff is the second step after you have already performed > > > > > the measurement. Hence not effecting your fit results and fit errors > > > > > (correct?!) > > > > > > > > This is not correct. Forget about 509 +- 44. You have to put together all > > > > numbers only after you will divide by each efficiency. > > > > > > > > Daniele > > > > > > > > > > > > > > Did you see my point? > > > > > > > > > > > > > > > Oliver > > > > > > > > > > On Mon, 29 Apr 2002, Daniele del Re wrote: > > > > > > > > > > > > > > > > > Hi, > > > > > > > > > > > > each category has a different efficiency. If you correct by the > > > > > > efficiency before putting together the results you will get a larger > > > > > > error. For instance: > > > > > > > > > > > > suppose to have just two categories > > > > > > > > > > > > eff(1) = 90% > > > > > > eff(2) = 10% > > > > > > > > > > > > while > > > > > > > > > > > > eff(overall) = 50% (same amount of events in both categories at the > > > > > > origin) > > > > > > > > > > > > Suppose to measure > > > > > > > > > > > > N(1) = 900 +- 30 > > > > > > N(2) = 100 +- 10 => > > > > > > > > > > > > Then > > > > > > > > > > > > N(1)_origin = 1000 +- 33 > > > > > > N(2)_origin = 1000 +- 100 => Ntot_origin = 2000 +- 105 > > > > > > > > > > > > > > > > > > while using just one category and one efficiency you get > > > > > > > > > > > > N = 1000 +- 32 => (eff = 50%) > > > > > > > > > > > > Ntot_origin = 2000 +- 64 > > > > > > > > > > > > > > > > > > The effect depends on the difference in the efficiencies and on the the > > > > > > number of events in each category. > > > > > > > > > > > > > > > > > > Since in our categorization we have two "bad" categories (the last two, > > > > > > ch3ne1 and ch3ne2) with small efficiencies and containing a pretty > > > > > > large fraction of events at the origin, the final result can have a much > > > > > > different error. > > > > > > > > > > > > > > > > > > Daniele > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > On Mon, 29 Apr 2002, Oliver Buchmueller wrote: > > > > > > > > > > > > > > > > > > > > Hi Daniele, > > > > > > > > > > > > > > thanks for the quick answer. This 20-30% difference was actually > > > > > > > the trigger for me to look more carefully to your results from the first > > > > > > > place. I just have difficulties to understand why a simple > > > > > > > (- assume statistically independent-) categorization can blow > > > > > > > up your fit error. > > > > > > > Looking at your numbers of fitted events and just adding the > > > > > > > the errors in quadrature I get 509+-44.3 events for the categorization > > > > > > > whereas you quote 559 +- 44 for no cat. . There is no 20-30% effect. > > > > > > > Are I am missing something (e.g. categories are not independent ..?) > > > > > > > > > > > > > > > > > > > > > Oliver > > > > > > > > > > > > > > > > > > > > > On Mon, 29 Apr 2002, Daniele del Re wrote: > > > > > > > > > > > > > > > > > > > > > > > Hi Oliver, > > > > > > > > > > > > > > > > thanks for your good comment. > > > > > > > > > > > > > > > > > ^ ^ > > > > > > > > > Are the two BR results | | > > > > > > > > > obtained from the same MC sample? > > > > > > > > > If yes, what has caused the shift? > > > > > > > > > > > > > > > > > > > > > > > > > As you see in general there is an increase of 20-30% in the error (due to > > > > > > > > categories with low statistics). This means that the two results can be > > > > > > > > different. > > > > > > > > > > > > > > > > In this particular case > > > > > > > > > > > > > > > > sqrt ( (sigma*1.3)^2 - sigma^2) ) ~ .8 sigma > > > > > > > > > > > > > > > > and 0.0179 - 0.0156 = .0023 = 1.6 * .0014(=sigma(ratio)) > > > > > > > > > > > > > > > > So this result is 1.6 sigma off. > > > > > > > > Looking in detail > > > > > > > > > > > > > > > > * signal events from the fit w/o categories: > > > > > > > > > > > > > > > > S = 559 +- 44 > > > > > > > > > > > > > > > > > > > > > > > > * signal events from the fit with categories: > > > > > > > > > > > > > > > > S S from truth > > > > > > > > > > > > > > > > 32 +- 7 115 > > > > > > > > 31 +- 12 93 > > > > > > > > 220 +- 20 662 > > > > > > > > 190 +- 28 594 > > > > > > > > 15 +- 15 108 > > > > > > > > 21 +- 19 144 > > > > > > > > > > > > > > > > total 509 1716 > > > > > > > > > > > > > > > > > > > > > > > > The lack comes from the last two categories and they weight more since > > > > > > > > they have a small efficiency. I don't see a fitting problem in these fits > > > > > > > > > > > > > > > > http://www.slac.stanford.edu/~daniele/vub/MCmulti/newMCshapech3ne1fitresults.eps > > > > > > > > http://www.slac.stanford.edu/~daniele/vub/MCmulti/newMCshapech3ne2fitresults.eps > > > > > > > > > > > > > > > > BTW I will look into the problem more in detail. > > > > > > > > > > > > > > > > Thanks a lot, > > > > > > > > > > > > > > > > Daniele > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > >