Program for assessment of the centrality, certainty interims and points of confinement by direct probabilities computati.


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Program for assessment of the essentialness, certainty interims and cutoff points by direct probabilities counts S.Bityukov (IHEP,Protvino) , S.Erofeeva(MSA IECS,Moscow), N.Krasnikov(INR RAS, Moscow) , A.Nikitenko(IC, London)
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Slide 1

Program for assessment of the hugeness, certainty interims and points of confinement by direct probabilities figurings S.Bityukov (IHEP,Protvino) , S.Erofeeva(MSA IECS,Moscow), N.Krasnikov(INR RAS, Moscow) , A.Nikitenko(IC, London) September, 2005 PhyStat 2005 Oxford, UK S.Bityukov

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Introduction During arranging or handling of investigation we regularly consider a measurable theory H 0 : new material science is available in Nature against speculation H 1 : new material science is missing in Nature . The estimation of vulnerability in our decision is characterized by the probabilities  = P(reject H 0 | H 0 is genuine) - Type I lapse and b = P(accept H 0 | H 0 is false) - Type II blunder There are numerous meanings of essentialness as a measure of abundance of sign occasions above foundation. Numerous methodologies exist likewise to routines for development of interims and points of confinement: certainty, tolerant, fiducial etc. Amid one of the CMS gatherings Gunter Quast planned the issue of practicians “the just remaining issue: settle on a decision … picked system ought to be “ as basic as could be expected under the circumstances, however not wrong !” September, 2005 PhyStat 2005 Oxford, UK S.Bityukov

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Motivation of the work (criticalness) Gaussian point of confinement gives the wrong response for low estimation of β (tail of Poisson appropriation is heavier than tail of Gaussian ) 2. The measurements like S L (a probability proportion based test measurement) have poor factual properties as estimator of centrality ( S L = √2•(ln L1-ln L2)= √2•(ln Q), where Q is the proportion of binned/unbinned probability fits for speculations H 0 and H 1 H 0 : sign present and H 1 : no sign present) The least difficult noteworthiness is the criticalness S_cP portrayed at the following slide. The S_cP is very normal centrality , which permits to consider any vulnerabilities by direct figuring of probabilities. September, 2005 PhyStat 2005 Oxford, UK S.Bityukov

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Definition of the criticalness S_cP - likelihood from Poisson appropriation with mean μ_ b to watch equivalent or more prominent than Nobs occasions, changed over to proportionate number of sigmas of a Gaussian dispersion (see report (page 8) by G. Quast in CMS Physics examination days, May 9-12, 2005, CERN http://cmsdoc.cern.ch/~bityukov/talks/talks.html likewise, see I.Narsky, NIM A450(2000)444). The displayed project ScP permits to ascertain this essentialness with considering exploratory systematics with factual properties ( Gaussian rough guess) and hypothetical systematics with no measurable properties. Likewise, the system figures (if alternative is on) the joining hugeness of a few channels. As is expected all channels are free. September, 2005 PhyStat 2005 Oxford, UK S.Bityukov

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Conception. The likelihood of making a Type II lapse ( β ) in speculations test about vicinity of sign in analysis ( H0 ) is utilized for determination number of sigmas (of foundation conveyance) between expected foundation and watched number of occasions Nobs (recipe 8 in CMS CR 2002/05 ). This likelihood is utilized for determination of sign criticalness, i.e. the essentialness S_cP will be found under determining of mathematical statements , where It can be utilized as a part of consolidating of results. Give us a chance to consider two conceivable methodologies. September, 2005 PhyStat 2005 Oxford, UK S.Bityukov

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Combining of watched results: Approach 1 Approach 1. Assume that watched quality is more noteworthy than anticipated foundation Let β _1 be Type II blunder for channel 1 (occasion A = foundation  Nobs _1 with P( A )= β _1 ) and β _2 be Type II mistake for channel 2 (occasion B = foundation  Nobs _2 with P( B )= β _2 ). Since occasion An is free from occasion B then likelihood of synchronous appearance of An and B meets β _12 = P( AB ) = P( A )*P( B ) = β _1* β _2 . After determination of β _12 one can compute the S_cP . September, 2005 PhyStat 2005 Oxford, UK S.Bityukov

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Combining of expected signs & foundations: Approach 2 Approach 2. Assume that Nobs is normal aggregate of expected sign ( μ_ s ) and expected foundation ( μ_b ), i.e. Nobs = μ_ s+ μ_b (the instance of arranged trial). At that point the wholes of expected quantities of sign ( μ_s_i ) and foundation ( μ_b_i ) occasions in every channel are utilized as rundown μ_s and μ_b for count of consolidated criticalness. Note that we consider for this situation as change of expected foundation and vacillation of expected sign. After determination of relating β one can ascertain the S_cP . September, 2005 PhyStat 2005 Oxford, UK S.Bityukov

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Uncertainties The project considers two sorts of instabilities: exploratory systematics with measurable properties (we accept that this systematics has Gaussian dispersion with known fluctuation σ _b**2 in concurring with recipe μ_ b = expected foundation + N (0, σ _b) ). Appr.2: For the joining\'s situation of channels the outline difference σ _b**2 is the total of fractional change σ _b_i**2 . b) hypothetical systematics ( Î\' _b ) with no factual properties (we expect: the most pessimistic scenario happens when the foundation is maximal, i.e. μ_ b*(1+ Î\' _b) , however we take the sign in addition to the foundation as Nobs ; more data can be found in S.Bityukov, N.Krasnikov, CMS CR 2002/05 or S.Bityukov, N.Krasnikov, Mod.Phys.Lett.A 13 (1998)3235) Appr.2: The consolidating Î\' _b is the entirety of halfway Î\' _b_i . September, 2005 PhyStat 2005 Oxford, UK S.Bityukov

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Main data and yield parameters Main information parameters: 1. expected foundation – μ_ b 2. signal = watched worth ( Nobs ) - expected foundation ( μ_ b ) – μ_ s 3. exploratory vulnerability ( r.m.s.) of foundation with measurable properties – σ_ b 4. systematics of hypothetical root in foundation – Î\'_ b Output parameters: 1. importance S_cP , ascertained by equation - dsgnf 2. noteworthiness S_cP_MC , computed by Monte Carlo - dsgnfm September, 2005 PhyStat 2005 Oxford, UK S.Bityukov

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Auxiliary info parameters 1. switch for picking of sort counts - iflag = 1 figurings by recipe (snappy computations) iflag = 2 Monte Carlo estimations iflag = 12 estimations by equation and by Monte Carlo 2. number of channels for figurings - nchan (from 1 up to 10 ) 3. number of channels for joined S_cP - ncombi (from 1 up to nchan ) 4. parameter for Monte Carlo estimation - over - parameter for Monte Carlo figurings. It is various Monte Carlo trials which will give estimation of number occasions over or break even with Nobs . This parameter (and inward esteem dbeta ) decides the quantity of trials for given μ_ s, μ_ b, σ _b and Î\'_ b in routine SCPMC . September, 2005 PhyStat 2005 Oxford, UK S.Bityukov

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The structure of system Language: Fortran 77 iflag Three distinct sorts 1. SCPFOR - figurings by recipe of computations: 2. SCPMC - Monte Carlo counts 12. SCPFOR + SCPMC Main project forms the client prerequisites (characterized in administrators DATA) and calls schedules SCPFOR and/or SCPMC . September, 2005 PhyStat 2005 Oxford, UK S.Bityukov

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Problem and rough guess The issue which happens amid computations is the limited scope of materialness of standard method DGAUSN in CERNLIB . For estimations of S_cP>6.2-7 the strategy gives non right result. For this situation we use as a decent close estimation the hugeness (MPL A13 (1998)3235) S_c12 = 2 ( ( μ_ s+ μ_b) -  μ_ b) . The instabilities\' record is extremely straightforward: hypothetical systematics ( Î\' _b ) S_c12t = 2 ( ( μ_ s+ μ_b) - ( μ_ b(1+ Î\' _b)) . test systematics ( σ _b**2 )  μ_ b S_c12e = 2 ( ( μ_ s+ μ_b) -  μ_ b) - - . ( μ_ b+ σ _b**2) September, 2005 PhyStat 2005 Oxford, UK S.Bityukov

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Simplest sample of project S_cP yield Example of G.Quast: bkg= 2 sig= 5.4 . Here S 1 =3.8 S 12 =2.6 S L =2.7 Significance S_cP and/or S_cP_MC: NN of channels = 1 , Combining channels